1989 Fiscal Year Annual Research Report

数値解析と応用解析の総合的研究

Research Project

Project/Area Number	01302007
Research Institution	Chiba University
Principal Investigator	河原田秀夫千葉大学, 工学部, 教授 (90010793)
Co-Investigator(Kenkyū-buntansha)	西田孝明京都大学, 理学部, 教授 (70026110) 三好哲彦山口大学, 工学部, 教授 (60040101) 菊地文雄東京大学, 教養学部, 教授 (40013734) 篠原能材徳島大学, 工学部, 教授 (40035803) 牛島照夫電気通信大学, 電気通信学部, 教授 (10012410)
Keywords	数値解析 / 有限要素法 / 高速自動微分法 / 丸め誤差 / 自由境界 / 最適形状設計 / 分岐現象 / 粘性流体
Research Abstract	1.各分担者の成果をもとに、研究集会「応用数学合同シンポジウム」を京都大学数理解析休究所において、平成元年12月18日(月)-20日(水)の間、開催した。そこでの報告は43報告で「応用数学合同シンポジウム研究報告集」として出版された。その内容は広範囲にわたるが、主なものをあげると次の通りである。 (i)数値解析(連立一次方程式におけるランク落ちの場合のCR法。有限要素法による三次元ポテンシャル問題の誤差評価や亀裂進展の解析) (ii)応用解析(最適形状設計問題。非線型問題に対する回有値問題。分岐現象とその解析) 2.更に、各研究分担者は各人の役割分担にそった論文として多数発表しているが、その内容を列挙すると以下の通りになる。偏微分と高速自動微分法における丸め誤差。非線型方程式に対する反復法の収束性及び数値計算。自由境界の有限要素解析とその視覚化・水の波偏差分方程式の固有値問題とその境界要素計算。traveling waveの安定性。reaction-diffusion systemにおけるwave blocking現象の解析。亀裂進展の数値計算。常微分方程式の数値解の研究。電磁場の偏微分方程式の有限要素解析。粘性流体及びガス方程式の研究。非線型固有値問題及び楕円型境界値問題の研究などである。 3.この科研費による研究の効果の一端が研究集会「先端技術における数理科学的諸問題の解明」(京都大学数理解析研究所、平成元年12月21日-22日)の開催と密接な係わりがあり、各研究分担者間の研究交流を進めると同時に、各研究分担者と大学の純粋数学専攻研究者及び民間の情報処理・シミュレ-ション・コミピュ-タ開発の研究者との交流が盛んになり、新しい分野を開きつつある。

Research Products
(51 results)

All Other

All Publications (51 results)

[Publications] H.Kawarada,T.Sawaguri & H.Imai: "An Approximate Resolution of a Free Boundary Problem Appearing in the Equilibrium Plasma by Means of Conformal Mapping" Japan J.Appl.Math.6(3). 331-340 (1989)
[Publications] 一松信: "コンピュ-タと数学との関連-大学段階の実例を中心に" 数学セミナ-増刊(数学教育とコンピュ-タ). 144-148 (1989)
[Publications] Kokichi SUGIHARA and Masao IRI: "Two design principles of geometric algorithms in finiteprescision arithmetic." Applied Mathematics Letters.2. 203-206 (1989)
[Publications] Kazuo KISHIMOTO and Masao IRI: "A practical approach to the definition and measurement of "length"." Japan Journal Applied Mathematics.6. 179-207 (1989)
[Publications] Masao IRI: "Aspects of combinatorial approaches to circuits and systems." Proceedings of the 1989 International Conference on Circuits and Systems.1-4 (1989)
[Publications] 伊理正夫、久保田光一: "数値計算の基礎技術の最近の話題から-ノルム、丸め誤差、偏微分と高速自動微分法を中心として" 電子情報通信学会. 72. 1044-1052 (1989)
[Publications] 伊理正夫: "正実関数と数値計算" 電子情報通信学会技術研究報告. 89. 77-84 (1990)
[Publications] T.Yamamoto: "Unified convergence analysis for a class of iterative methods for solving nonlinear equations" Topics in Mathematical Anlysis(Edited by T.M.Rassias) A Volume Dedicated to the Memory of A.L.Cauchy(World Sci.). 878-900 (1989)
[Publications] X.Chen T.Yamamoto: "Convergence domains of certain iterative methods for solving nonlinear equations" Numer.Funct.Anal.and Optim. 10. 37-48 (1989)
[Publications] T.Yamamoto X.Chen: "An existence and nonexistence theorem for solutions of nonlinear systens and its application to algebraic equations" J.of Comp.and Appl.Math.(1990)
[Publications] T.Yamamoto X.Chen: "Ball-convergence theorems and error estimates for certain iterative methods for nonlinear equations" Japan J.Appl.Math.7. 131-143 (1990)
[Publications] 山本哲朗,陳小君: "有限次元非線形方程式に対する保証付き数種計算" 情報処理. (1990)
[Publications] Y.Yamamoto S.Takigawa: "Transient and large time behaviors of solutions of a size-space distribution model including chemotactic aggregation" Japan J.Appl.Math.6. 223-244 (1989)
[Publications] M.Mori,M.Natori and Zhang Guo Feng: "A finite element analysis of a free surface drainage problem of two immiscible fluids" International Journal for Numerical Methods in Fluids. 9. 569-582 (1989)
[Publications] M.Mori: "Visualization of the residual polynomials of the CG and the ICCG methods" Proceedings of the international Symposium on Numerical Analysis. 257-271 (1989)
[Publications] H.Kanayama,T.Ushijima: "On the viscous shallow-water equations III,-a finite elemet scheme" Bulletin of the University of Electro-Communications. 2巻1号. 47-62 (1989)
[Publications] 牛島照夫、松木美保子、青木篤: "水の波の線形問題について" 数理解析研究所講究録. 691. 97-125 (1989)
[Publications] 牛島照夫、若松宏明: "水の波の線形固有値問題の境界要素計算" 数理解析研究所講究録. 703. 46-63 (1989)
[Publications] 松木美保子、牛島照夫、: "水の波偏差分方程式の固有問題" 数理解析研究所講究録「自由境界問題とその周辺」. 1. (1990)
[Publications] 大森克史、牛島照夫: "ラックス・ヴェンドルフ型有限要素スキ-ムの数学解析" 第3回計算力学シンポジウム報文集. 105-110 (1989)
[Publications] 名古屋靖一郎、牛島照夫: "空間一次元移流拡散スキ-ムの安定性解析" 第3回数値流体力学シンポジウム講演論文集. 243-246 (1989)
[Publications] Y.Nishiura,M.Mimura,H.Ikeda & H.Fujii: "Singular limit analysis of stability of traveling wave solutions in bistable reaction-diffusion systems(to appear)" SIAM J.Math Anal.
[Publications] H.Fujii,Y.Nishiura & M.Miura: "Bifurcations of raveling waves"
[Publications] H.Fujii,& M.Mimura: "Hopf bifurcations of traveling waves"
[Publications] Y.Nishiura & H.Fujii: "Instability of plangr fronts in reaction-diffusion systems"
[Publications] H.Fujii: "Instability of traveling fronts in phase field model of solidification"
[Publications] A.KOHDA and Y.SHINOHARA: "On uniform limit of quasiperiodic functions" J.Math.Tokushima Univ.23. 39-40 (1989)
[Publications] Y.SHINOHARA: "On numerically integrable solutions of ordinary differential equations" J.Math.Tokushima Univ.23. 41-44 (1989)
[Publications] Y.Nishiura,M.Mimura: "Layer oscillations in reaction-diffusion systems" SIAM Journal on Applied Mathematics. 49. 481-514 (1989)
[Publications] H.Ikeda,M.Mimura: "Wave blocking phenomena in bistable reaction-diffusion systems" SIAM Journal on applied Mathematics. 49. 515-539 (1989)
[Publications] Y.Hosono,M.Mimura: "Localized cluster solutions of nonlinear degenerate diffusion equations arising in population dynamics" SIAM Jornal on Mathematical Analysis. 20. 845-869 (1989)
[Publications] T.Ohta,M.Mimura & R.Kobayashi: "Higher dimensional localized patterns in excitable media" Physica D. 34. 115-144 (1989)
[Publications] S.Ei,M.Mimura: "Pattern formation in heterogeneous reaction-diffusion advection systems with an application to population dynamics" SIAM Journal on Mathematical Analysis(to appear). (1990)
[Publications] F.Kikuchi: "Weak formulations for finite element analysis of an electromagnetic eigenvalue problem" Scientific Papers of the college of Arts and Sciences,The University of Tokyo. 38. 43-67 (1989)
[Publications] F.Kikuchi: "Mixed formulations for finite element analysis of magnetostatic and electrostatic problems" Japan Journal of Applied Mathematics. 6. 209-221 (1989)
[Publications] F.Kikuchi: "On a discrete compactness property for the Nedelec finite elements" Journal of the Faculty of Science,The University of Tokyo,Sec.IA. 36. 479-490 (1989)
[Publications] T.Yamada,A.Wada,F.Kikuchi: "A 9-node mixed shell element based on the Hu-Washizu principle" Theoretical and Applied Mechanics. 38. 81-91 (1990)
[Publications] 三好哲彦、藤本新平: "亀裂進展の数値計算について" 応用数学合同シンポジウム研究報告集. 46-51 (1989)
[Publications] T.Nishida,A.Matsumura: "Exterior stationary problem for the equations of motion of compressible,viscous and heat-conductive fluids" Differential Equations,Lecture Notes in Pure and Appl.Math.,ed.by Dafermis,Marcel Dekher Inc.118. 473-479 (1989)
[Publications] T.Nishida,A.Matsumura: "Periodic solutions of a viscous gas equation" Recent Topics in Nonlinear PDE IV ed.by Mimura & Nishida,Kinokuniya/North Holland. 160. 49-82 (1989)
[Publications] K.Narukawa,T.Suzuki: "Nonlinear eigenvalue problem associated to capillary surfaces" Boll.U.M.I.
[Publications] K.Nagasaki,T.Suzuki: "Radial and nonradial solutions for the nonlinear eigenvalue problem △u+λe^u=0 on annuli in R^2" J.Differential Equations.
[Publications] K.Nagasaki,T.Suzuki: "Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially-dominated nonlinearities" Asymptotic Analysis.
[Publications] K.Nagasaki,T.Suzuki: "Nonlinear eigenvalue problem△u+λe^u=0 on simply connected domains in R^2" Proc.Japan Acad.Ser.A. 65. 1-3 (1989)
[Publications] K.Nagasaki,T.Suzuki: "Asymptotic behavior of the solution for an elliptic boundary value problem with exponential nonlinearity" Proc.Japan Acad.Ser.A. 65. 74-76 (1989)
[Publications] 河原田秀夫: "自由境界問題" 東大出版会, 131 (1989)
[Publications] 一松信: "√<2>の数学" 海鳴社, 116 (1990)
[Publications] 一松信: "微分積分学入門第一課" 近代科学社, 184 (1989)
[Publications] Masao IRI and Kunio TANABE(編): "Mathematical Programming---Recent Developments and Applications." Kluwer Academic Publishers., Viii+382 (1989)
[Publications] 小野寺嘉孝、森正武他: "Fortran77による数値計算ソフトウエア" 丸善株式会社, 325 (1989)
[Publications] H.Fujita T.Suzuki: "Lectures on Finite Element Method for Evolution problems(to appear)" Elserier(P.G.Ciarlet & J.L.Lions.eds.),

1989 Fiscal Year Annual Research Report

数値解析と応用解析の総合的研究

Principal Investigator

河原田 秀夫 千葉大学, 工学部, 教授 (90010793)

Research Products

[Publications] H.Kawarada,T.Sawaguri & H.Imai: "An Approximate Resolution of a Free Boundary Problem Appearing in the Equilibrium Plasma by Means of Conformal Mapping" Japan J.Appl.Math.6(3). 331-340 (1989)

[Publications] 一松信: "コンピュ-タと数学との関連-大学段階の実例を中心に" 数学セミナ-増刊(数学教育とコンピュ-タ). 144-148 (1989)

[Publications] Kokichi SUGIHARA and Masao IRI: "Two design principles of geometric algorithms in finiteprescision arithmetic." Applied Mathematics Letters.2. 203-206 (1989)

[Publications] Kazuo KISHIMOTO and Masao IRI: "A practical approach to the definition and measurement of "length"." Japan Journal Applied Mathematics.6. 179-207 (1989)

[Publications] Masao IRI: "Aspects of combinatorial approaches to circuits and systems." Proceedings of the 1989 International Conference on Circuits and Systems.1-4 (1989)

[Publications] 伊理正夫、久保田光一: "数値計算の基礎技術の最近の話題から-ノルム、丸め誤差、偏微分と高速自動微分法を中心として" 電子情報通信学会. 72. 1044-1052 (1989)

[Publications] 伊理正夫: "正実関数と数値計算" 電子情報通信学会 技術研究報告. 89. 77-84 (1990)

[Publications] T.Yamamoto: "Unified convergence analysis for a class of iterative methods for solving nonlinear equations" Topics in Mathematical Anlysis(Edited by T.M.Rassias) A Volume Dedicated to the Memory of A.L.Cauchy(World Sci.). 878-900 (1989)

[Publications] X.Chen T.Yamamoto: "Convergence domains of certain iterative methods for solving nonlinear equations" Numer.Funct.Anal.and Optim. 10. 37-48 (1989)

[Publications] T.Yamamoto X.Chen: "An existence and nonexistence theorem for solutions of nonlinear systens and its application to algebraic equations" J.of Comp.and Appl.Math.(1990)

[Publications] T.Yamamoto X.Chen: "Ball-convergence theorems and error estimates for certain iterative methods for nonlinear equations" Japan J.Appl.Math.7. 131-143 (1990)

[Publications] 山本哲朗,陳小君: "有限次元非線形方程式に対する保証付き数種計算" 情報処理. (1990)

[Publications] Y.Yamamoto S.Takigawa: "Transient and large time behaviors of solutions of a size-space distribution model including chemotactic aggregation" Japan J.Appl.Math.6. 223-244 (1989)

[Publications] M.Mori,M.Natori and Zhang Guo Feng: "A finite element analysis of a free surface drainage problem of two immiscible fluids" International Journal for Numerical Methods in Fluids. 9. 569-582 (1989)

[Publications] M.Mori: "Visualization of the residual polynomials of the CG and the ICCG methods" Proceedings of the international Symposium on Numerical Analysis. 257-271 (1989)

[Publications] H.Kanayama,T.Ushijima: "On the viscous shallow-water equations III,-a finite elemet scheme" Bulletin of the University of Electro-Communications. 2巻1号. 47-62 (1989)

[Publications] 牛島照夫、松木美保子、青木篤: "水の波の線形問題について" 数理解析研究所講究録. 691. 97-125 (1989)

[Publications] 牛島照夫、若松宏明: "水の波の線形固有値問題の境界要素計算" 数理解析研究所講究録. 703. 46-63 (1989)

[Publications] 松木美保子、牛島照夫、: "水の波偏差分方程式の固有問題" 数理解析研究所講究録「自由境界問題とその周辺」. 1. (1990)

[Publications] 大森克史、牛島照夫: "ラックス・ヴェンドルフ型有限要素スキ-ムの数学解析" 第3回計算力学シンポジウム報文集. 105-110 (1989)

[Publications] 名古屋靖一郎、牛島照夫: "空間一次元移流拡散スキ-ムの安定性解析" 第3回数値流体力学シンポジウム講演論文集. 243-246 (1989)

[Publications] Y.Nishiura,M.Mimura,H.Ikeda & H.Fujii: "Singular limit analysis of stability of traveling wave solutions in bistable reaction-diffusion systems(to appear)" SIAM J.Math Anal.

[Publications] H.Fujii,Y.Nishiura & M.Miura: "Bifurcations of raveling waves"

[Publications] H.Fujii,& M.Mimura: "Hopf bifurcations of traveling waves"

[Publications] Y.Nishiura & H.Fujii: "Instability of plangr fronts in reaction-diffusion systems"

[Publications] H.Fujii: "Instability of traveling fronts in phase field model of solidification"

[Publications] A.KOHDA and Y.SHINOHARA: "On uniform limit of quasiperiodic functions" J.Math.Tokushima Univ.23. 39-40 (1989)

[Publications] Y.SHINOHARA: "On numerically integrable solutions of ordinary differential equations" J.Math.Tokushima Univ.23. 41-44 (1989)

[Publications] Y.Nishiura,M.Mimura: "Layer oscillations in reaction-diffusion systems" SIAM Journal on Applied Mathematics. 49. 481-514 (1989)

[Publications] H.Ikeda,M.Mimura: "Wave blocking phenomena in bistable reaction-diffusion systems" SIAM Journal on applied Mathematics. 49. 515-539 (1989)

[Publications] Y.Hosono,M.Mimura: "Localized cluster solutions of nonlinear degenerate diffusion equations arising in population dynamics" SIAM Jornal on Mathematical Analysis. 20. 845-869 (1989)

[Publications] T.Ohta,M.Mimura & R.Kobayashi: "Higher dimensional localized patterns in excitable media" Physica D. 34. 115-144 (1989)

[Publications] S.Ei,M.Mimura: "Pattern formation in heterogeneous reaction-diffusion advection systems with an application to population dynamics" SIAM Journal on Mathematical Analysis(to appear). (1990)

[Publications] F.Kikuchi: "Weak formulations for finite element analysis of an electromagnetic eigenvalue problem" Scientific Papers of the college of Arts and Sciences,The University of Tokyo. 38. 43-67 (1989)

[Publications] F.Kikuchi: "Mixed formulations for finite element analysis of magnetostatic and electrostatic problems" Japan Journal of Applied Mathematics. 6. 209-221 (1989)

[Publications] F.Kikuchi: "On a discrete compactness property for the Nedelec finite elements" Journal of the Faculty of Science,The University of Tokyo,Sec.IA. 36. 479-490 (1989)

[Publications] T.Yamada,A.Wada,F.Kikuchi: "A 9-node mixed shell element based on the Hu-Washizu principle" Theoretical and Applied Mechanics. 38. 81-91 (1990)

[Publications] 三好哲彦、藤本新平: "亀裂進展の数値計算について" 応用数学合同シンポジウム研究報告集. 46-51 (1989)

[Publications] T.Nishida,A.Matsumura: "Exterior stationary problem for the equations of motion of compressible,viscous and heat-conductive fluids" Differential Equations,Lecture Notes in Pure and Appl.Math.,ed.by Dafermis,Marcel Dekher Inc.118. 473-479 (1989)

[Publications] T.Nishida,A.Matsumura: "Periodic solutions of a viscous gas equation" Recent Topics in Nonlinear PDE IV ed.by Mimura & Nishida,Kinokuniya/North Holland. 160. 49-82 (1989)

[Publications] K.Narukawa,T.Suzuki: "Nonlinear eigenvalue problem associated to capillary surfaces" Boll.U.M.I.

[Publications] K.Nagasaki,T.Suzuki: "Radial and nonradial solutions for the nonlinear eigenvalue problem △u+λe^u=0 on annuli in R^2" J.Differential Equations.

[Publications] K.Nagasaki,T.Suzuki: "Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially-dominated nonlinearities" Asymptotic Analysis.

[Publications] K.Nagasaki,T.Suzuki: "Nonlinear eigenvalue problem△u+λe^u=0 on simply connected domains in R^2" Proc.Japan Acad.Ser.A. 65. 1-3 (1989)

[Publications] K.Nagasaki,T.Suzuki: "Asymptotic behavior of the solution for an elliptic boundary value problem with exponential nonlinearity" Proc.Japan Acad.Ser.A. 65. 74-76 (1989)

[Publications] 河原田秀夫: "自由境界問題" 東大出版会, 131 (1989)

[Publications] 一松信: "√<2>の数学" 海鳴社, 116 (1990)

[Publications] 一松信: "微分積分学入門第一課" 近代科学社, 184 (1989)

[Publications] Masao IRI and Kunio TANABE(編): "Mathematical Programming---Recent Developments and Applications." Kluwer Academic Publishers., Viii+382 (1989)

[Publications] 小野寺嘉孝、森正武他: "Fortran77による数値計算ソフトウエア" 丸善株式会社, 325 (1989)

[Publications] H.Fujita T.Suzuki: "Lectures on Finite Element Method for Evolution problems(to appear)" Elserier(P.G.Ciarlet & J.L.Lions.eds.),

河原田秀夫千葉大学, 工学部, 教授 (90010793)

[Publications] 伊理正夫: "正実関数と数値計算" 電子情報通信学会技術研究報告. 89. 77-84 (1990)