1990 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, Faculty of Engineering
Principal Investigator	河原田秀夫千葉大学, 工学部, 教授 (90010793)
Co-Investigator(Kenkyū-buntansha)	鈴木貴東京都立大学, 理学部, 助教授 (40114516) 森正武東京大学, 工学部, 教授 (20010936) 伊理正夫東京大学, 工学部, 教授 (40010722) 藤田宏明治大学, 理工学部, 教授 (80011427) 山口昌哉龍谷大学, 理工学部, 教授 (30025796)
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	科学研究費補助金による2年間の研究が大きな成果を得て終了した。この間の研究実績については、印刷物「数値解析と応用解析の総合的研究」研究成果報告書(代表者河原田秀夫)にまとめて、この報告書に添付している。なお、今年度については、各研究分担者の研究成果をもとに研究集会「応用数学合同研究集会」を京都大学数理解析研究所と京都大学理学部において、平成2年12月17日(月)ー19日(水)の間、開催した。そこでの報告は59件で、「応用数学合同研究集会報告集」として、発表されている。この研究集会における各研究分担者の間の研究交流は、数値解析と応用解析との整合的な発展に多大の寄与があった。そのことが上記の研究成果報告書の内容にもなっている。なお、研究集会の主な内容は次の通りである。 1.多項式の因数分解 2.有限代数(1),(2) 3.セル・オ-トマトン 4.プログラミング 5.流れの理論 6.反応拡散方程式7.論法と解法 8.構造解析 9.流れの計算 10.パタ-ン 11.アルゴリズム 12.Maxwell方程式 13.楕円型方程式 14.逆問題 15.結晶 16.コンピュ-テ-ション

Research Products
(29 results)

All Other

All Publications (29 results)

[Publications] H.IMAI,H.KAWARADA: "A method for finding bifurcattion points" Control and cybernetics(to appear). 19(3). (1990)
[Publications] A.SASAMOTO,H.IMAI,H.KAWARADA: "A practical method for an illーconditioned optimal shape design of a vessel in which plasma is confined" (submitted).
[Publications] H.KAWARADA,H.KOSHIGOE: "The unsteady flow in the porous media with a free surface" J.J.Ind.Appl.Math. 8(1). 41-82 (1991)
[Publications] H.Fujita,T.Suzuki: "Evolution Problems" Handbook of Numerical Analysis vol.11,Finite Element Methods(Part 1),Elsevier Science Publishers B.V.11. 791-928 (1991)
[Publications] 山口昌哉: "新しい応用数学と技術" 計測と制御(5月). 29(5). 449-458 (1990)
[Publications] 山口昌哉,山田道夫: "ウェ-ブレット解析" 科学(6月). 398-405 (1990)
[Publications] M.Iri: "Automatic differentiation and rounding error estimationーOverview and History." SIAM Workshop on“Automatic Differentiation of AlgorithmsーTheory,Implementation,and Application",January 6ー8 Breckenridge,Colorado,U.S.A.(1991)
[Publications] K.Kishimoto,M.Iri: "A practical approach to the definition and measurement of“length"." Japan Journal of Applied Mathematics. 6(2). 179-207 (1989)
[Publications] T.Yamamoto and X.Chen: "Ballーconvergence theorems and error estimates for certain iterative methods for nonlinear equations" Japan J.Appl.Math.7. 7. 131-143 (1990)
[Publications] T.Yamamoto and X.Chen: "An existence and nonexistence theorem for solutions of nonlinear systems and its application to algebraic equations" J.Computational and Applied Mathematics.30. 30. 87-97 (1990)
[Publications] M.Mori: "Developments in the double exponential formulas for numerical integration," to appear in the Proceedings of the International Congress of Mathematicians,Kyoto,SpringerーVerlag.(1990)
[Publications] S.Fujino,M.Mori,T.Takeuchi: "Performance of hyperplane ordering on vector computers" submitted to J.Comput.Appl.Math.
[Publications] 松木美保子、牛島照夫: "水の波偏差分方程式の固有値問題、自由境界問題の数値解析とその周辺" 数理解析研究所講究録. 724. 154-177 (1990)
[Publications] Y.Nishiura,M.Mimura,H.Ikeda and H.Fujii: "Singular limit analysis of stability of travelling wave solutions in bistable reactionーdiffusion systems" SIAM J.Math.Appl.21(1). 85-122 (1990)
[Publications] H.Fujii,Y.Nishiura,M Mimura & R.Kobayashi: "Instability of Planar Traveling Fronts in Phase Field Model of Solidifications" to appear in Proc.U.S.ーJapan Seminar 1989. (1989)
[Publications] S.ーI.Ei and M.Mimura: "Pattern formation in heterogeneous reactionーdiffusionーadvection systems with an application to population dynamics" Appl.Math.21. 346-361 (1990)
[Publications] D.Hilhorse,Y.Nishiura,M.Mimura: "A free boundary problem arising from some reactionーdiffusion system," to appear in Proc.Royal Soc.Edinburgh.
[Publications] Y.SHINOHARA: "On the quasiperiodic solutions to nonlinear quasiperiodic differential equations" Abstracts of ICMー90. 187. (1990)
[Publications] T.Yamada,F.Kikuchi: "A mixed finite element method for large deformation analysis of incompressible hyperelastic materials" Theo.Appl.Mech.39. 61-73 (1990)
[Publications] T.Yamada,F.Kikuchi,A.Wada: "A 9ーnode mixed shell element based on the HuーWashizu principle" to appear in Comput.Mech.
[Publications] K.Kaminishi,T.Miyoshi,M.Taneda: "A consistent explicit scheme for dynamic plasticity problems" Proceedings of ICES Greece '91.
[Publications] T.Miyoshi: "Semidiscrete systems in plasticity" Proceedings of Atenes Interdisciplinary Olympia '91. (1991)
[Publications] A.Matsumura,T.Nishida: "Periodic solutions in the half space for a oneーdimensional model of viscoーelasticity." RIMS Kyoto University. (1991)
[Publications] M.Okada and T.Nishida: "On the NeumannーRichtmyer method for the free boundary problem of a oneーdimensional motion of viscous gas." Nonlinear PDE,Japan Symposium,Kinokuniya/NorthーHolland. (1991)
[Publications] T.Suzuki: "Introduction to geometric potential theory" FunctionalーAnalytic Methods for Partial Differential Equations,Lecture Notes in Math Springer,Berlin et.al.1450. 88-103 (1990)
[Publications] T.Suzuki,K.Nagasaki: "Radial and nonradial solutions for the nonlinear eigenvalue problem Δu+λe^u=Ο on annului in 〓^2" J.Differential Equations. 87. 144-168 (1990)
[Publications] 藤田宏,黒田成俊,伊藤清三: "関数解析" 岩波書店, 526 (1991)
[Publications] 藤田宏,吉田耕作: "現代解析入門" 岩波書店, 457 (1991)
[Publications] 森正武: "FORTRAN77図形処理プログラミング" 岩波書店, (1991)

1990 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.IMAI,H.KAWARADA: "A method for finding bifurcattion points" Control and cybernetics(to appear). 19(3). (1990)

[Publications] A.SASAMOTO,H.IMAI,H.KAWARADA: "A practical method for an illーconditioned optimal shape design of a vessel in which plasma is confined" (submitted).

[Publications] H.KAWARADA,H.KOSHIGOE: "The unsteady flow in the porous media with a free surface" J.J.Ind.Appl.Math. 8(1). 41-82 (1991)

[Publications] H.Fujita,T.Suzuki: "Evolution Problems" Handbook of Numerical Analysis vol.11,Finite Element Methods(Part 1),Elsevier Science Publishers B.V.11. 791-928 (1991)

[Publications] 山口 昌哉: "新しい応用数学と技術" 計測と制御(5月). 29(5). 449-458 (1990)

[Publications] 山口 昌哉,山田 道夫: "ウェ-ブレット解析" 科学(6月). 398-405 (1990)

[Publications] M.Iri: "Automatic differentiation and rounding error estimationーOverview and History." SIAM Workshop on“Automatic Differentiation of AlgorithmsーTheory,Implementation,and Application",January 6ー8 Breckenridge,Colorado,U.S.A.(1991)

[Publications] K.Kishimoto,M.Iri: "A practical approach to the definition and measurement of“length"." Japan Journal of Applied Mathematics. 6(2). 179-207 (1989)

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

[Publications] T.Yamamoto and X.Chen: "An existence and nonexistence theorem for solutions of nonlinear systems and its application to algebraic equations" J.Computational and Applied Mathematics.30. 30. 87-97 (1990)

[Publications] M.Mori: "Developments in the double exponential formulas for numerical integration," to appear in the Proceedings of the International Congress of Mathematicians,Kyoto,SpringerーVerlag.(1990)

[Publications] S.Fujino,M.Mori,T.Takeuchi: "Performance of hyperplane ordering on vector computers" submitted to J.Comput.Appl.Math.

[Publications] 松木 美保子、牛島 照夫: "水の波偏差分方程式の固有値問題、自由境界問題の数値解析とその周辺" 数理解析研究所講究録. 724. 154-177 (1990)

[Publications] Y.Nishiura,M.Mimura,H.Ikeda and H.Fujii: "Singular limit analysis of stability of travelling wave solutions in bistable reactionーdiffusion systems" SIAM J.Math.Appl.21(1). 85-122 (1990)

[Publications] H.Fujii,Y.Nishiura,M Mimura & R.Kobayashi: "Instability of Planar Traveling Fronts in Phase Field Model of Solidifications" to appear in Proc.U.S.ーJapan Seminar 1989. (1989)

[Publications] S.ーI.Ei and M.Mimura: "Pattern formation in heterogeneous reactionーdiffusionーadvection systems with an application to population dynamics" Appl.Math.21. 346-361 (1990)

[Publications] D.Hilhorse,Y.Nishiura,M.Mimura: "A free boundary problem arising from some reactionーdiffusion system," to appear in Proc.Royal Soc.Edinburgh.

[Publications] Y.SHINOHARA: "On the quasiperiodic solutions to nonlinear quasiperiodic differential equations" Abstracts of ICMー90. 187. (1990)

[Publications] T.Yamada,F.Kikuchi: "A mixed finite element method for large deformation analysis of incompressible hyperelastic materials" Theo.Appl.Mech.39. 61-73 (1990)

[Publications] T.Yamada,F.Kikuchi,A.Wada: "A 9ーnode mixed shell element based on the HuーWashizu principle" to appear in Comput.Mech.

[Publications] K.Kaminishi,T.Miyoshi,M.Taneda: "A consistent explicit scheme for dynamic plasticity problems" Proceedings of ICES Greece '91.

[Publications] T.Miyoshi: "Semidiscrete systems in plasticity" Proceedings of Atenes Interdisciplinary Olympia '91. (1991)

[Publications] A.Matsumura,T.Nishida: "Periodic solutions in the half space for a oneーdimensional model of viscoーelasticity." RIMS Kyoto University. (1991)

[Publications] M.Okada and T.Nishida: "On the NeumannーRichtmyer method for the free boundary problem of a oneーdimensional motion of viscous gas." Nonlinear PDE,Japan Symposium,Kinokuniya/NorthーHolland. (1991)

[Publications] T.Suzuki: "Introduction to geometric potential theory" FunctionalーAnalytic Methods for Partial Differential Equations,Lecture Notes in Math Springer,Berlin et.al.1450. 88-103 (1990)

[Publications] T.Suzuki,K.Nagasaki: "Radial and nonradial solutions for the nonlinear eigenvalue problem Δu+λe^u=Ο on annului in 〓^2" J.Differential Equations. 87. 144-168 (1990)

[Publications] 藤田 宏,黒田 成俊,伊藤 清三: "関数解析" 岩波書店, 526 (1991)

[Publications] 藤田 宏,吉田 耕作: "現代解析入門" 岩波書店, 457 (1991)

[Publications] 森 正武: "FORTRAN77図形処理プログラミング" 岩波書店, (1991)

河原田秀夫千葉大学, 工学部, 教授 (90010793)

[Publications] 山口昌哉: "新しい応用数学と技術" 計測と制御(5月). 29(5). 449-458 (1990)

[Publications] 山口昌哉,山田道夫: "ウェ-ブレット解析" 科学(6月). 398-405 (1990)

[Publications] 松木美保子、牛島照夫: "水の波偏差分方程式の固有値問題、自由境界問題の数値解析とその周辺" 数理解析研究所講究録. 724. 154-177 (1990)

[Publications] 藤田宏,黒田成俊,伊藤清三: "関数解析" 岩波書店, 526 (1991)

[Publications] 藤田宏,吉田耕作: "現代解析入門" 岩波書店, 457 (1991)

[Publications] 森正武: "FORTRAN77図形処理プログラミング" 岩波書店, (1991)