1990 年度実績報告書

数値解析と応用解析の総合的研究

研究課題

研究課題/領域番号	01302007
研究機関	千葉大学
研究代表者	河原田秀夫千葉大学, 工学部, 教授 (90010793)
研究分担者	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)
キーワード	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
研究概要	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

研究成果

(29件)

すべてその他

すべて文献書誌 (29件)

[文献書誌] H.IMAI,H.KAWARADA: "A method for finding bifurcattion points" Control and cybernetics(to appear). 19(3). (1990)
[文献書誌] 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).
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] 山口昌哉,山田道夫: "ウェ-ブレット解析" 科学(6月). 398-405 (1990)
[文献書誌] 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)
[文献書誌] K.Kishimoto,M.Iri: "A practical approach to the definition and measurement of“length"." Japan Journal of Applied Mathematics. 6(2). 179-207 (1989)
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] S.Fujino,M.Mori,T.Takeuchi: "Performance of hyperplane ordering on vector computers" submitted to J.Comput.Appl.Math.
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] D.Hilhorse,Y.Nishiura,M.Mimura: "A free boundary problem arising from some reactionーdiffusion system," to appear in Proc.Royal Soc.Edinburgh.
[文献書誌] Y.SHINOHARA: "On the quasiperiodic solutions to nonlinear quasiperiodic differential equations" Abstracts of ICMー90. 187. (1990)
[文献書誌] T.Yamada,F.Kikuchi: "A mixed finite element method for large deformation analysis of incompressible hyperelastic materials" Theo.Appl.Mech.39. 61-73 (1990)
[文献書誌] 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.
[文献書誌] K.Kaminishi,T.Miyoshi,M.Taneda: "A consistent explicit scheme for dynamic plasticity problems" Proceedings of ICES Greece '91.
[文献書誌] T.Miyoshi: "Semidiscrete systems in plasticity" Proceedings of Atenes Interdisciplinary Olympia '91. (1991)
[文献書誌] A.Matsumura,T.Nishida: "Periodic solutions in the half space for a oneーdimensional model of viscoーelasticity." RIMS Kyoto University. (1991)
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] 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)
[文献書誌] 藤田宏,黒田成俊,伊藤清三: "関数解析" 岩波書店, 526 (1991)
[文献書誌] 藤田宏,吉田耕作: "現代解析入門" 岩波書店, 457 (1991)
[文献書誌] 森正武: "FORTRAN77図形処理プログラミング" 岩波書店, (1991)

1990 年度 実績報告書

数値解析と応用解析の総合的研究

研究代表者

河原田 秀夫 千葉大学, 工学部, 教授 (90010793)

研究成果

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

[文献書誌] 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).

[文献書誌] 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)

[文献書誌] 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)

[文献書誌] 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)

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

[文献書誌] 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)

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

[文献書誌] 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)

[文献書誌] 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)

[文献書誌] 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)

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

[文献書誌] 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)

[文献書誌] 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)

[文献書誌] 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)

[文献書誌] 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)

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

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

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

[文献書誌] 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.

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

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

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

[文献書誌] 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)

[文献書誌] 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)

[文献書誌] 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)

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

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

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

1990 年度実績報告書

河原田秀夫千葉大学, 工学部, 教授 (90010793)

[文献書誌] 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)

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

[文献書誌] 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)

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

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

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