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CONSERVATION AND STABILITY OF DYNAMICAL SYSTEMS AND ITS NUMERICAL ANAKYSIS

Research Project

Project/Area Number 15340029
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNAGOYA UNIVERSITY

Principal Investigator

MITUI Taketomo  Nagoya University, Grad. Sch. of Information Science, Professor, 大学院・情報科学研究科, 教授 (50027380)

Co-Investigator(Kenkyū-buntansha) OKADA Masami  Nagoya University, Fac. of Urban Liberal Arts, Tokyo Metropolitan Univ., Professor, 都市教養学部, 教授 (00152314)
KOTO Toshiyuki  Nagoya University, Grad. Sch. of Information Science, Assoc. Professor, 大学院・情報科学研究科, 助教授 (30234793)
SAKAJO Takashi  Hokkaido Univ., Grad. Sch. of Sci., Assoc. Professor, 大学院・理学研究科, 助教授 (10303603)
SUGIURA Hiroshi  Nanzan University, Fac. of Math. Sci. and Info. Eng., Professor, 数理情報学部, 教授 (60154465)
SUGIHARA Masaaki  University of Tokyo, Grad. Sch. of Info. Sci. and Tech., Professor, 大学院・情報理工学系研究科, 教授 (80154483)
石井 克哉  名古屋大学, 情報連携基盤センター, 教授 (60134441)
前田 茂  徳島大学, 総合科学部, 教授 (20115934)
Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥16,500,000 (Direct Cost: ¥16,500,000)
Fiscal Year 2005: ¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 2004: ¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 2003: ¥8,500,000 (Direct Cost: ¥8,500,000)
KeywordsComputational science / Numerical analysis / Dynamical systems / Stability / Conservative system / Discrete variable methods / Nonlinear equations / Eigenvalue analysis / 非線型方程式
Research Abstract

The project targets a study of dynamical systems from both analytical and numerical points of view with the emphasis on the conservation and the stability of the system. A typical mathematical formulation of dynamical system is attained through the Hamilton canonical form. Then its symplecticness has much significance in the theoretical as well as the numerical analysis. As such an interrelationship between analysis and numerics for the conservation property of dynamical systems has attracted many attentions of theorists and practitioners. The project was planned to carry out an in-depth study and to open new aspect of the topic. It can achieve the following items.
(1) Correspondence between continuous and discrete dynamical systems from numerical point of view
Recent development of the so-called discrete variational derivative (DVD) method sheds a new light upon the discrete variable numerical methods. DVD method can derive many finite difference methods for (nonlinear) partial differen … More tial equations to preserve its invariant quantities in a natural manner. Also a trial to extend the principle to the Galerkin-type numerical methods can attain a success.
(2) Interrelationship between numerical stability and numerical solution of conservation or dissipation type
Generally numerical stability is significant for numerical solutions of dynamical systems. It discriminates the conservation and the non-conservation of the solutions as well. As a typical example, a study of vortex sheet motion in fluid dynamics reveals the interrelationship and can give a precise diagram of the motion.
(3) Numerical analysis of dynamical system with time-delay or randomness
Many of delay differential equations and stochastic differential equations are dissipative. Then a question arises what role the numerical stability plays for these equations. Our study shows that the numerical stability is crucial for the solution, and consequently can endorse the numerical solution as simulation of the phenomena governed by such equations.
(4) Application of the study to large-scale simulations of the dynamical systems
Large-scale simulation of the system requires the stability more. Also, for a long-term integration of the system more accurate numerical schemes are called for. In some practical examples, like as eigenvalue analysis, computational fluid dynamics etc., which have practical significance, more sophisticated and powerful methods are developed. There parallel computation improves the performance much, under the condition of being stable, for numerical solution.
During the term of the project, an international conference, 2005 International Conference on Scientific Computation and Differential Equations (SciCADE05), was held in Nagoya with a good support of the project. More than 250 people, among whom around 170 were from overseas, joined the conference and exchanged new ideas each other. Most of their discussions were on the topic of the project. Less

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (121 results)

All 2006 2005 2004 2003 Other

All Journal Article (107 results) Book (7 results) Publications (7 results)

  • [Journal Article] 確率中点スキームのMS安定性について2006

    • Author(s)
      齋藤善弘
    • Journal Title

      Review of Economics and Information Studies 6 No3.4(掲載予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] MS-stability of the stochastic mid-point scheme2006

    • Author(s)
      Y.Saito, K.Takeuchi
    • Journal Title

      Review of Economics and Information Studies. 6 (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation2005

    • Author(s)
      B.-F.Feng
    • Journal Title

      Intern. J. Math. Math. Sci 2005

      Pages: 1435-1448

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Efficient topological chaos embedded in the blinking vortex system2005

    • Author(s)
      E.Kin
    • Journal Title

      Chaos 15

      Pages: 23111-23111

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Motion of unstable polygonal ring of vortex points on sphere with pole vortices2005

    • Author(s)
      T.Sakajo
    • Journal Title

      Proceedings of IUTAM Kyoto 2004

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] High-dimensional heteroclinic and homoclinic connections in odd point-vortex system on sphere with pole vortices2005

    • Author(s)
      T.Sakajo
    • Journal Title

      Nonlinearity 19

      Pages: 75-93

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 代数方程式に対する高次Nourein法の収束特性2005

    • Author(s)
      鈴木智博
    • Journal Title

      情報処理学会論文誌 46, No.10

      Pages: 2505-2512

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical solution of integral equations by means of the Sinc-collocation method based on the double exponential transformation2005

    • Author(s)
      M.Muhammad
    • Journal Title

      Journal of Computational and Applied Mathematics 177

      Pages: 269-286

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Double exponential transformation in the Sinc-collocation method for the boundary problem of fourth-order ordinary differential equation2005

    • Author(s)
      A.Nurmuhammad
    • Journal Title

      Journal of Computational and Applied Mathematics 182

      Pages: 32-50

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 共役残差法の非対称行列用への拡張2005

    • Author(s)
      曽我部知広
    • Journal Title

      日本応用数理学会論文誌 15

      Pages: 445459-445459

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical indefinite integration by double exponential sinc method2005

    • Author(s)
      K.Tanaka
    • Journal Title

      Mathematics of Computation 74

      Pages: 655-679

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Exponential functionals of Brownian motion, I : Probability laws at fixed time2005

    • Author(s)
      H.Matsumoto
    • Journal Title

      Probability Surveys 2

      Pages: 312-347

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Exponential functionals of Brownian motion, II : Some related diffusion processes2005

    • Author(s)
      H.Matsumoto
    • Journal Title

      Probability Surveys 2

      Pages: 348-384

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] キャッシュマシン向け対称密行列固有値解法の性能・精度評価2005

    • Author(s)
      山本有作
    • Journal Title

      情報処理学会論文誌ACS 46 No.SIG3

      Pages: 81-91

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 密行列固有値解法の最近の発展(I) - Multiple Relatively Robust Representations アルゴリズム -2005

    • Author(s)
      山本有作
    • Journal Title

      日本応用数理学会論文誌 15, No.2

      Pages: 181-208

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 2資産に依存するオプションの高速・高精度価格計算手法2005

    • Author(s)
      高柳健一郎
    • Journal Title

      情報処理学会論文誌ACS 46 No.SIG12

      Pages: 289-298

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Vector-Parallel Algorithms for 1-Dimensional Fast Fourier Transform, in New Horizons of Parallel and Distributed Computing2005

    • Author(s)
      Y.Yamamoto
    • Journal Title

      Kluwer Academic Publishers

      Pages: 2005-2005

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete path-Dependent Options2005

    • Author(s)
      M.Broadie
    • Journal Title

      Operations Research 53, No.5

      Pages: 764-779

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Double-Exponential Fast Gauss Transform Algorithms for Pricing Discrete Lookback Options2005

    • Author(s)
      Y.Yamamoto
    • Journal Title

      Publ. RIMS Kyoto Univ. 41

      Pages: 989-1006

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation2005

    • Author(s)
      B.-F.Feng, T.Kawahara, T.Mitsui, Y.-S.Chan
    • Journal Title

      Intern.J.Math.Math.Sci. 2005

      Pages: 1435-1448

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Efficient topological chaos embedded in the blinking vortex system2005

    • Author(s)
      E.Kin, T.Sakajo
    • Journal Title

      Chaos. 15

      Pages: 23111-23111

    • NAID

      120006459380

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Motion of unstable polygonal ring of vortex points on sphere with pole vortices2005

    • Author(s)
      T.Sakajo
    • Journal Title

      Proceedings of IUTAM Kyoto. 2004

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] High-dimensional heteroclinic and homoclinic connections in odd point-vortex system on sphere with pole vortices2005

    • Author(s)
      T.Sakajo
    • Journal Title

      Nonlinearity. 19

      Pages: 75-93

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical solution of integral equations by means of the Sinc-collocation method based on the double exponential transformation2005

    • Author(s)
      M.Muhammad, A.Nurmuhammad, M.Mori, M.Sugihara
    • Journal Title

      Journal of Computational and Applied Mathematics. 177

      Pages: 269-286

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Double exponential transformation in the Sinc-collocation method for the boundary problem of fourth-order ordinary differential equation2005

    • Author(s)
      A.Nurmuhammad, M.Muhammad, M.Mori, M.Sugihara
    • Journal Title

      Journal of Computational and Applied Mathematics. 182

      Pages: 32-50

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical indefinite integration by double exponential sinc method2005

    • Author(s)
      K.Tanaka, M.Sugihara, K.Murota
    • Journal Title

      Mathematics of Computation. 74

      Pages: 655-679

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Exponential functionals of Brownian motion, I : Probability laws at fixed time2005

    • Author(s)
      H.Matsumoto, M.Yor
    • Journal Title

      Probability Surveys. 2

      Pages: 312-347

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Exponential functionals of Brownian motion, II : Some related diffusion processes2005

    • Author(s)
      H.Matsumoto, M.Yor
    • Journal Title

      Probability Surveys. 2

      Pages: 348-384

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Vector-Parallel Algorithms for 1-Dimensional Fast Fourier Transform, in New Horizons of Parallel and Distributed Computing2005

    • Author(s)
      Y.Yamamoto, H.Kawamura, M.Igai
    • Journal Title

      Kluwer Academic Publishers

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete path-Dependent Options2005

    • Author(s)
      M.Broadie, Y.Yamamoto
    • Journal Title

      Operations Research. 53, No.5

      Pages: 764-779

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Double-Exponential Fast Gauss Transform Algorithms for Pricing Discrete Lookback Options2005

    • Author(s)
      Y.Yamamoto
    • Journal Title

      Publ.RIMS Kyoto Univ. 41

      Pages: 989-1006

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Convergence property of higher order Nourein's method for algebraic equations2005

    • Author(s)
      T.Suzuki, H.Sugiura
    • Journal Title

      Journal IPSJ. 46

      Pages: 2505-2512

    • NAID

      110002769898

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] An extension of the conjugate residual method for solving nonsymmetric linear systems2005

    • Author(s)
      T.Sogabe, M.Sugiura, S.-L.Zhang
    • Journal Title

      Trans.JSIAM. 15

      Pages: 445-459

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Performance and accuracy of algorithms for computing the eigenvalues of real symmetric matrices on cache-based microprocessors2005

    • Author(s)
      Y.Yamamoto
    • Journal Title

      Trans.IPSJ. ACS8

      Pages: 81-91

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Recent developments in solving dense eigenproblems (I)-Algorithm of multiple relatively robust represeutations2005

    • Author(s)
      Y.Yamamoto
    • Journal Title

      Trans.JSIAM. 15

      Pages: 181-208

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A fast and accurate algorithm for pricing options on two assets2005

    • Author(s)
      K.Takayanagi, Y.Yamamoto, M.Sugihara
    • Journal Title

      Trans.IPSJ. ACS12

      Pages: 289-298

    • NAID

      110002769845

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation2005

    • Author(s)
      B.-F.Feng
    • Journal Title

      International Journal of Mathematics and Mathematical Sciences 2005

      Pages: 1435-1448

    • Related Report
      2005 Annual Research Report
  • [Journal Article] High-dimensional heteroclinic and homoclinic connections in odd point-vortex system on sphere with pole vortices2005

    • Author(s)
      Takashi Sakajo
    • Journal Title

      Nonlinearity 19

      Pages: 75-93

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 代数方程式に対する高次Nourein法の収束特性2005

    • Author(s)
      鈴木智博
    • Journal Title

      情報処理学会論文誌 46

      Pages: 2505-2512

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Numerical indefinite integration by double exponential sinc method2005

    • Author(s)
      Ken-ichiro Tanaka
    • Journal Title

      Mathematics of Computation 74

      Pages: 655-679

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Exponential functionals of Brownian motion, I : Probability laws at fixed time2005

    • Author(s)
      Hiroyuki Matsumoto
    • Journal Title

      Probability Surveys 2

      Pages: 312-347

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Double-exponential fast Gauss transform algorithms for pricing discrete lookback options2005

    • Author(s)
      Yusaku Yamamoto
    • Journal Title

      Publications of RIMS, Kyoto Univ. 41

      Pages: 989-1006

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A double-exponential fast Gauss transform algorithms for pricing discrete path-dependent options2005

    • Author(s)
      M.Broadie, Y.Yamamoto
    • Journal Title

      Operations Research (to appear)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Semi-discretization method along the charactersitics for linear advection-diffusion equations2004

    • Author(s)
      Nobuyuki Esaki
    • Journal Title

      Southeast Asian Bulletin of Mathematics 27

      Pages: 813-827

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Parallelizable block Rosenbrock methods for linear variable-coefficient system of ODEs2004

    • Author(s)
      Nobuyuki Esaki
    • Journal Title

      IPSJ Transactions on Advanced Computing Systems 45 SIG11 (ACS7)

      Pages: 290-302

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A variant of the Orthomin(2) method for singular linear systems2004

    • Author(s)
      K.Abe
    • Journal Title

      Numer. Algorithms 36

      Pages: 189-202

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Hamiltonian formulation of energy conservative Variational integration by wavelet expansion2004

    • Author(s)
      S.Maeda
    • Journal Title

      J. of Funct. Anal 209

      Pages: 414-424

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Generalized energy integrals and energy conserving numerical schemes for partial differential equations2004

    • Author(s)
      C.Hirota
    • Journal Title

      Japan J. Indust.Appl. Math 21

      Pages: 163-179

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Method of lines approximations of delay differential equations2004

    • Author(s)
      Toshiyuki Koto
    • Journal Title

      Compt. Math. Appl 48

      Pages: 393-404

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 丸山簡易スキームの数値的安定性2004

    • Author(s)
      齋藤善弘
    • Journal Title

      Review of Economics and Information Studies 5 No1.2

      Pages: 99-110

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Motion of a vortex sheet on a sphere with pole vortices2004

    • Author(s)
      T.Sakajo
    • Journal Title

      Physics of Fluids 16

      Pages: 717-727

    • NAID

      120000954515

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Analytic continuation of the Birkhoff-Rott equation in complex time domain2004

    • Author(s)
      T.Sakajo
    • Journal Title

      European J. Appl. Math 15

      Pages: 639-659

    • NAID

      120000957213

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices2004

    • Author(s)
      T.Sakajo
    • Journal Title

      Physica D 196

      Pages: 243-264

    • NAID

      120000958318

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 解析関数の多項式因子を求める精度保証付き解法2004

    • Author(s)
      牛 暁明
    • Journal Title

      日本応用数理学会論文誌 14

      Pages: 59-73

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 代用電荷法による数値等角写像とポテンシャル流問題への応用2004

    • Author(s)
      天野 要
    • Journal Title

      情報処理学会論文誌 45

      Pages: 1322-1325

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Recent developments of the Sinc numerical methods2004

    • Author(s)
      M.Sugihara
    • Journal Title

      Journal of Computational and Applied Mathematics 164-165

      Pages: 673-689

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Markov or non-Markov property of $cM-X$ processes2004

    • Author(s)
      H.Matsumoto
    • Journal Title

      J. Math. Soc. Japan 56

      Pages: 519-540

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws2004

    • Author(s)
      H.Matsumoto
    • Journal Title

      Publ. RIMS, Kyoto Univ. 40

      Pages: 1385-1412

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 高速ガウス変換を用いた天候デリバティブの価格評価手法2004

    • Author(s)
      山本有作
    • Journal Title

      情報処理学会論文誌ACS 45 NO.SIG6

      Pages: 176-185

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Semi-discretization method along the characteristics for linear advection-diffusion equations2004

    • Author(s)
      N.Esaki, T.Mitsui, F.A.Oliveira, F.Patricio
    • Journal Title

      Southeast Asian Bulletin of Mathematics 27

      Pages: 813-827

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Parallelizable block Rosenbrock methods for linear variable-coefficient system of ODEs2004

    • Author(s)
      N.Esaki, T.Mitsui
    • Journal Title

      IPSJ Trans.Advanced Computing Systems 45, SIG 11 (ACS 7)

      Pages: 290-302

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A variant of the Orthomin(2) method for singular linear systems2004

    • Author(s)
      K.Abe, S.-L.Zhang, T.Mitsui, C.-H.Jin
    • Journal Title

      Numer.Algorithms 36

      Pages: 189-202

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Generalized energy integrals and energy conserving numerical schemes for partial differential equations.2004

    • Author(s)
      C.Hirota, T.Ide, N.Fukuoka, M.Okada
    • Journal Title

      Japan J.Indust.Appl.Math. 21

      Pages: 163-179

    • NAID

      10018379954

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Method of lines approximations of delay differential equations2004

    • Author(s)
      Toshiyuki Koto
    • Journal Title

      Comput.Math.Appl. 48

      Pages: 393-404

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Recent developments of the Sinc numerical methods2004

    • Author(s)
      M.Sugihara, T.Matsuo
    • Journal Title

      Journal of Computational and Applied Mathematics 164-165

      Pages: 673-689

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Hamiltonian formulation of energy conservative variational equations by wavelet expansion2004

    • Author(s)
      S.Maeda, M.Okada
    • Journal Title

      J.Func.Anal. 209

      Pages: 414-424

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Analytic continuation of the Birkhoff-Rott equation in complex time domain2004

    • Author(s)
      T.Sakajo
    • Journal Title

      European J.Appl.Math. 15

      Pages: 639-659

    • NAID

      120000957213

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices2004

    • Author(s)
      T.Sakajo
    • Journal Title

      Physica D. 196

      Pages: 243-264

    • NAID

      120000958318

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Markov or non-Markov property of $cM-X$ processes2004

    • Author(s)
      H.Matsumoto, Y.Ogura
    • Journal Title

      J.Math.Soc.Japan. 56

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws2004

    • Author(s)
      H.Matsumoto, C.Donati-Martin, Y.Doumerc, M.Yor
    • Journal Title

      Publ.RIMS, Kyoto Univ. 41

      Pages: 1385-1412

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical stability of the simplified Euler-Maruyama scheme2004

    • Author(s)
      Y.Saito
    • Journal Title

      Review of Economics and Information Studies. 5

      Pages: 99-110

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A verified method for finding polynomial factors of analytic functions2004

    • Author(s)
      X.-M.Nu, T.Sakurai, H.Sugiura
    • Journal Title

      Trans.JSIAM. 14

      Pages: 59-73

    • NAID

      110001878245

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical conformal mappings by the charge simulation method and their application to potential flow problems2004

    • Author(s)
      K.Amano, M.Tamai, D.Okano, H.Ogata, M.Sugiura
    • Journal Title

      Journal IPSJ. 45

      Pages: 1322-1325

    • NAID

      110002712181

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Valuation of weather derivatives using the fast Gauss transform2004

    • Author(s)
      Y.Yamamoto, M.Egi
    • Journal Title

      Trans.IPSJ. ACS6

      Pages: 176-185

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Parallelizable block Rosenbrock methods for linear variable-coefficient system of ODEs2004

    • Author(s)
      N.Esaki, T.Mitsui
    • Journal Title

      IPSJ Trans.Advanced Computing Systems 45 SIG 11

      Pages: 290-302

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Generalized energy integrals and energy conserving conserving numerical schemes for partial differential equations2004

    • Author(s)
      C.Hirota, T.Ide, N.Fukuoka, M.Okada
    • Journal Title

      Japan J.Indust.Appl.Math. 21

      Pages: 163-179

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Method of lines approximations of delay differential equations2004

    • Author(s)
      Toshiyuki Koto
    • Journal Title

      Comput.Math.Appl 48

      Pages: 393-404

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Motion of a vortex sheet on a sphere with pole vortices2004

    • Author(s)
      Takashi Sakajo
    • Journal Title

      Physics of Fluids 16

      Pages: 717-727

    • NAID

      120000954515

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Recent developments of the Sinc numerical method2004

    • Author(s)
      M.Sugihara, T.Matsuo
    • Journal Title

      J.Comput.Appl.Math. 164-165

      Pages: 673-689

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Predator-prey dynamics with delay when prey dispersing in $n$-patch environment2003

    • Author(s)
      L.Qiu
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 20

      Pages: 37-49

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Parallel predictor-corrector iteration of pseudo two-step RK methods for nonstiff IVPs2003

    • Author(s)
      Nguyen huu Cong
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 20

      Pages: 51-64

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A fast solver of the shallow water equation on a sphere using a combined compact difference scheme2003

    • Author(s)
      T.Nihei
    • Journal Title

      Journal of Computational Physics 187

      Pages: 639-659

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A wavelet collocation method for evolution equations with energy conservation property2003

    • Author(s)
      T.Ueno
    • Journal Title

      Bull. Sci. Math 127

      Pages: 569-583

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stability of $theta$-methods for delay integro-differential equation2003

    • Author(s)
      Toshiyuki Koto
    • Journal Title

      J. Comput. Appl. Math 161

      Pages: 393-404

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Blow-up solutions of Constantin-Lax-Majda equation with a generalized viscosity term2003

    • Author(s)
      T.Sakajo
    • Journal Title

      J. Math. Sci. Univ. Tokyo 10

      Pages: 187-207

    • NAID

      110003948133

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On global solutions of Constantin-Lax-Majda equation with a generalized viscosity term2003

    • Author(s)
      T.Sakajo
    • Journal Title

      Nonlinearity 16

      Pages: 1319-1328

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A projection method for generalized eigenvalue problems using numerical integration2003

    • Author(s)
      Tetsuya Sakurai
    • Journal Title

      J. Comput. Appl. Math 159 No.1

      Pages: 119-128

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A perturbation result for generalized eigenvalue problems and its application to error estimation in a quadrature method for computing zeros of analytic functions2003

    • Author(s)
      Peter Kravanja
    • Journal Title

      J. Comput. Appl. Math 161, No.2

      Pages: 339-347

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A fundamental solution method for viscous flow problems with obstacles in a periodic array2003

    • Author(s)
      H.Ogata
    • Journal Title

      Journal of Computational and Applied Mathematics 152

      Pages: 411-425

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical conformal mappings of bounded multiply-connected domains2003

    • Author(s)
      D.Okano
    • Journal Title

      Journal of Computational and Applied Mathematics 159

      Pages: 109-117

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Interpretation via Brownian motion of some independence properties between GIG and gamma variables2003

    • Author(s)
      H.Matsumoto
    • Journal Title

      Stat. Prob. Lett. 61

      Pages: 253-259

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts2003

    • Author(s)
      H.Matsumoto
    • Journal Title

      J. Appl. Prob. 35

      Pages: 184-206

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Predator-prey dynamics with delay when preydispersing in n-patch environment2003

    • Author(s)
      L.Qiu, T.Mitsui
    • Journal Title

      Japan J.Industr.Appl.Math. 20

      Pages: 37-49

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Parallel predictor-corrector iteration of pseudo two-step RK methods for nonstiff IVPs2003

    • Author(s)
      Nguyen huu Cong, T.Mitsui
    • Journal Title

      Japan J.Industr.Appl.Math. 20

      Pages: 51-64

    • NAID

      10018380341

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A fast solver of the shallow water equation on a sphere using a combined compact difference scheme2003

    • Author(s)
      T.Nihei, K.Ishii
    • Journal Title

      Journal of Computational Physics. 187

      Pages: 639-659

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A wavelet collocation method for evolution equations with energy conservation property2003

    • Author(s)
      T.Ueno, T.Ide, M.Okada
    • Journal Title

      Bull.Sci.Math. 127

      Pages: 569-583

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stability of $theta$-methods for delay integro-differential equation2003

    • Author(s)
      Toshiyuki Koto
    • Journal Title

      J.Comput.Appl.Math. 161

      Pages: 393-404

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Blow-up solutions of Constantin-Lax-Majda equation with a generalized viscosity term2003

    • Author(s)
      T.Sakajo
    • Journal Title

      J.Math.Sci.Univ.Tokyo. 10

      Pages: 187-207

    • NAID

      110003948133

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A projection method for generalized eigenvalue problems using numerical integration2003

    • Author(s)
      Tetsuya Sakurai, Hiroshi Sugiura
    • Journal Title

      J.Comput.Appl.Math. 159, No.1

      Pages: 119-128

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A perturbation result for generalized eigenvalue problems and its application to error estimation in a quadrature method for computing zeros of analytic functions2003

    • Author(s)
      Peter Kravanja, Tetsuya sakurai, Hiroshi Sugihara, Marc Van Barel
    • Journal Title

      J.Comput.Appl.Math. 161, no.2

      Pages: 339-347

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A fundamental solution method for viscous flow problems with obstacles in a periodic array2003

    • Author(s)
      H.Ogata, K.Amano, M.Sugihara, D.Okano
    • Journal Title

      Journal of Computational and Applied Mathematics. 152

      Pages: 411-425

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical conformal mappings of bounded multiply-connected domains2003

    • Author(s)
      D.Okano, H.Ogata, K.Amano, M.Sugihara
    • Journal Title

      Journal of Computational and Applied Mathematics. 159

      Pages: 109-117

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Interpretation via Brownian motion of some independence properties between GIG and gamma variables2003

    • Author(s)
      H.Matsumoto, M.Yor
    • Journal Title

      Stat.Prob.Lett. 61

      Pages: 253-259

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts2003

    • Author(s)
      H.Matsumoto, M.Yor
    • Journal Title

      J.Appl.Prob. 35

      Pages: 184-206

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On global solutions of Constantin-Lax-Majda equation with a generalized viscosity term2003

    • Author(s)
      T.Sakajo
    • Journal Title

      Nonlinearity. 16

      Pages: 1319-1328

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical Simulation for Nonlinear Partial Differential Equation with Variable Coefficients by Means of the Discrete Variational Derivative Method

    • Author(s)
      T.Ide
    • Journal Title

      J. Comput. Appl. Math To appear

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Numerical Simulation for Nonlinear Partial Differential Equation with Variable Coefficients By Means of the Discrete Variational Derivative Method

    • Author(s)
      T.Ide, M.Okada
    • Journal Title

      J.Comput.Appl.Math. (To Appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] 数値計算のわざ2006

    • Author(s)
      二宮 市三
    • Total Pages
      171
    • Publisher
      共立出版
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Book] The Skills of Numerical Computations2006

    • Author(s)
      I.Ninomiya others
    • Publisher
      Kyoritsu Publishers
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] 微分方程式による計算科学入門2004

    • Author(s)
      三井斌友
    • Total Pages
      213
    • Publisher
      共立出版
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] 数値計算のつぼ2004

    • Author(s)
      二宮 市三
    • Total Pages
      171
    • Publisher
      共立出版
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] Introduction to Computational Science through Differential Equations2004

    • Author(s)
      T.Mitsui, T.Koto, Y.Saito
    • Publisher
      Kyoritsu Publishers
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] The Points of Numerical Computations2004

    • Author(s)
      I.Ninomiya others
    • Publisher
      Kyoritsu Publishers
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Book] 微分方程式による計算科学入門2004

    • Author(s)
      三井斌友, 小藤俊幸, 齋藤善弘
    • Total Pages
      213
    • Publisher
      共立出版
    • Related Report
      2004 Annual Research Report
  • [Publications] M.Sugihara, T.Matsuo: "Recent developments of the Sine numerical methods"Journal of Computational and Applied Mathematics. (to appear). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Koto: "Stability of $\$theta$-methods for delay integro-differential equations"Journal of Computational and Applied Mathematics. 161. 393-404 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Sakajo: "Motion of a vortex sheet on a sphere with pole vortices"Phys.Fluids. (in press). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] P.Kravanja, T.Sakurai, H.Sugiura, A.Van Barel: "A perturbation result for generalized eigenvalue problems and its application to error estimation in a quadrature method for computing zeros of analytic functions"Journal of Computational and Applied Mathematics. 161. 339-347 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Nihei, K.Ishii: "A Fast solver of the Shallow Water Equations on a Sphere using a Combined Compact Difference Scheme"Journal of Computational Physics. 187. 639-659 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Shigeru Maeda, Masami Okada: "Hamiltonian formulation of energy conservative variational integration by wavelet expansion"Journal of Functional Analysis. (to appear). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 三井斌友, 小藤俊幸, 齊藤善弘: "微分方程式による計算科学入門"共立出版. 213 (2004)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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