1991 Fiscal Year Annual Research Report

微分方程式の関数解析的及び数値解析的研究

Research Project

Project/Area Number	03640134
Research Institution	The University of Electro-Communications
Principal Investigator	梅津聰電気通信大学, 電気通信学部, 助教授 (80017409)
Co-Investigator(Kenkyū-buntansha)	渡辺二郎電気通信大学, 電気通信学部, 教授 (90011535) 内藤敏機電気通信大学, 電気通信学部, 教授 (60004446) 田吉隆夫電気通信大学, 電気通信学部, 教授 (60017382) 田端正久電気通信大学, 電気通信学部, 教授 (30093272) 牛島照夫電気通信大学, 電気通信学部, 教授 (10012410)
Keywords	発展方程式 / 有限要素法 / シコレ-ディンガ-方程式 / 関数微分方程式 / 高いレイノルズ数流れ / 自由境界問題 / 磁気流体方程式 / ルンゲ・クッタ法
Research Abstract	1.水の波の初期値問題を時間軸で差分近似,空間軸で有限要素法で近似,収束性と誤差の解析を与えた。又,スキムの拡張を与えた(牛島) 2.(1)対称化有限要素法を移流拡散方程式へ適用,URR機計算の実用性を示した。(2)水の自由境界問題のLagrange要素近似で良好な結果を得た。(3)高精度上流近似を高Reynolds流れに適用した(田端)。 3.Schrodinger作用素の正固有値非存在のための条件を求めた(田吉)。 4.無限遅れを持つ関数微分方程式に関する共役半郡及び関数微分方程式の解の漸近安定性について成果が得られた(内藤)。 5.石鹸膜について,解の分岐,安定性について数値結果が得られ,新しい知見が得られた(渡辺)。 6.変数成分の行列のブロック対角化について結果を得た(平沢)。 7.低抵性MHO方程式のスペクトル及びその常微分方程式モデルの近似スペクトルの数値近似について知見が得られた(加古)。 8.ガロア拡大についてのBelyiの論文についての結果を得た(小嶋)。 9.群上Involution及び球面関数のEuler型積分公式の結果を得た(関口)。 10.応用上頻出する微分代数系の高精度陰的ルンゲクッタ法の理論について成果を得た(小藤)。 11.磁気ベナ-ル問題の分岐解の存在証明,常微分方程式系モデルの提案及びその数値実験,それらの検討を行った(中村)。 12.水の凝固に対し,密度変化を考慮したモデルを提案し,その数値実験及びその検討を行った(花田)。 13.上流型有限要素近似を分担者田端と共に高Roynolds流れに適用,良い結果を得た。円柱まわりの流れで多くの成果を得た(藤間)。 14.多孔領域の境界上半線形境界条件を満たすPoisson方程式の解の漸近挙動について多くの知見を得た(海津)。

Research Products

(25 results)

All Other

All Publications (25 results)

[Publications] Ushijima Teruo: "Computational aspect of linear water wave problem." Journal of Computational and Applied Mathematics. 38. 425-445 (1991)
[Publications] Ushijima Teruo,Matsuki Mihoko: "Fully discrete approximation of a second order linear evolution equation related to the water wave problem" Abstract of International Conference on Functional Analysis and Related Topics(held at RIMS Kyoto Univ.). 17-18 (1991)
[Publications] Tabata M,Ozeki Y.: "Symmetric finite element computution of convectionーdiffusion equations on a URR machine" Japan Journal of Industrial and Applied Mathematics. 8. 153-163 (1991)
[Publications] 田端正久,小林俊雄: "自由境界問題のラグランジュ有限要素近似" 「自由境界問題の数値解析とその周辺」京都大学数理解析研究所講究録. 744. 15-28 (1991)
[Publications] Tabata M,Fujima S.: "Am upwind finite element scheme for highーReynoldsーnumber flows" International Journal of Numerical Methods on Fluids. 12. 305-322 (1991)
[Publications] Tayoshi Takao: "Nonーexistence of positive eigenvalues of the Sehrodinger operator in a domain with unbounded boundary" Journal of Mathematics of Kyoto University. 31. 467-485 (1991)
[Publications] Naito Toshiki: "Asymptotic stability of linear functional differential equations with the fading memory space" Proc.of the International Symposium on Functional Differential Equations,World Scientific. 269-273 (1991)
[Publications] Naito Toshiki: "Dual semigroups associated with linear functional differential equations with infinite delay" To appear in the Proc.of Equadiff 91,Barcelond.
[Publications] 渡辺二郎: "石けん膜の安定性をめぐって" 応用数理. 2(1号). (1992)
[Publications] Hirasawa Yoshikazu: "On a global blockーdiagonalisation of square matrices with variable components" Bulletin of the univesity of electroーcommunications. 5.
[Publications] Kako,T and Descloux,J.: "Spectral approximation for the linearized MHD operator in cylindrical region" Japan J.Indust.Appl.Math.8. 221-244 (1991)
[Publications] Kako,T.: "Spectral and numerical analysis for resisitive magnetohydrodynamic operators" ICIA91,Abstracts. 102 (1991)
[Publications] Kojima Hisashi: "Remark on Belyi's paper concerning Galois extensions of the maximal cyclotomic field with certain linear groups as Galois groups" Tohoku Mathematical Journal. 43. 117-122 (1991)
[Publications] 長野正,関口次郎: "Commuting Involutions of Semisimple Groups" Tokyo Journal of Mathematics. 14. 319-327 (1991)
[Publications] 関口次郎: "An Euler Type Integral Formula for Zonal Spherical Functions on SO。(m,2)/SO(m) SO(2)" Bulletin of the University of ElectroーCommunications. 4. 87-103 (1991)
[Publications] 小藤俊幸: "指数2の微分ー代数系の数値解法における簡約Newton法" 情報処理学会論文誌. 32. 133-139 (1991)
[Publications] Koto T.: "ThirdーOrder SemiーImplicit RungeーKutta Methods for TimeーDependent IndexーOne DifferentialーAlgebraic Equations" J.of Information Processing. 14. 172-177 (1991)
[Publications] Nakamura M.: "On the Magnetic Benard Problew" J.Fac.Sci.Univ.Tokyo,Sec.IA. 38. 359-393 (1991)
[Publications] Nakamura M.: "On an Equilibrium of the Plasma in a Tokamak with Limiter" Japan J.of Ind.Appl.Math.8. 431-444 (1991)
[Publications] 花田孝郎,今井仁司,河原田秀夫,名取亮: "凝固現象の数値解析" 数理解析研究所講究録「Phase transitionと最適制御」. (1992)
[Publications] 花田孝郎,今井仁司,河原田秀夫,名取亮: "体積変化と接触点の運動を考慮したステファン問題の数値解析" 応用数学合同シンポジウム(京都大学・数理解析研究所). (1991)
[Publications] Tabata M,Fujima S.: "Finiteーelement analysis of high Reynolds number flows past a circular cylinder" J.of Computational and Applied Mathematics. 38. 411-424 (1991)
[Publications] Kaizu S.: "The Poisson equation in domains with many tiny cracks" International Congress of Mathematicians,Abstracts,Short Communications,Kyoto,Japan,August. 168 (1991)
[Publications] Kaizu S.: "The Poisson equation with nonautonomous semilinear boundary conditions in domains with many tinyholes" SIAM J. Math. Anal.22. 1222-1245 (1991)
[Publications] 田端正久(分担執筆): "現代数理科学辞典" 大阪書店, 1310(8) (1991)

1991 Fiscal Year Annual Research Report

微分方程式の関数解析的及び数値解析的研究

Principal Investigator

梅津 聰 電気通信大学, 電気通信学部, 助教授 (80017409)

Research Products

[Publications] Ushijima Teruo: "Computational aspect of linear water wave problem." Journal of Computational and Applied Mathematics. 38. 425-445 (1991)

[Publications] Ushijima Teruo,Matsuki Mihoko: "Fully discrete approximation of a second order linear evolution equation related to the water wave problem" Abstract of International Conference on Functional Analysis and Related Topics(held at RIMS Kyoto Univ.). 17-18 (1991)

[Publications] Tabata M,Ozeki Y.: "Symmetric finite element computution of convectionーdiffusion equations on a URR machine" Japan Journal of Industrial and Applied Mathematics. 8. 153-163 (1991)

[Publications] 田端 正久,小林 俊雄: "自由境界問題のラグランジュ有限要素近似" 「自由境界問題の数値解析とその周辺」京都大学数理解析研究所講究録. 744. 15-28 (1991)

[Publications] Tabata M,Fujima S.: "Am upwind finite element scheme for highーReynoldsーnumber flows" International Journal of Numerical Methods on Fluids. 12. 305-322 (1991)

[Publications] Tayoshi Takao: "Nonーexistence of positive eigenvalues of the Sehrodinger operator in a domain with unbounded boundary" Journal of Mathematics of Kyoto University. 31. 467-485 (1991)

[Publications] Naito Toshiki: "Asymptotic stability of linear functional differential equations with the fading memory space" Proc.of the International Symposium on Functional Differential Equations,World Scientific. 269-273 (1991)

[Publications] Naito Toshiki: "Dual semigroups associated with linear functional differential equations with infinite delay" To appear in the Proc.of Equadiff 91,Barcelond.

[Publications] 渡辺 二郎: "石けん膜の安定性をめぐって" 応用数理. 2(1号). (1992)

[Publications] Hirasawa Yoshikazu: "On a global blockーdiagonalisation of square matrices with variable components" Bulletin of the univesity of electroーcommunications. 5.

[Publications] Kako,T and Descloux,J.: "Spectral approximation for the linearized MHD operator in cylindrical region" Japan J.Indust.Appl.Math.8. 221-244 (1991)

[Publications] Kako,T.: "Spectral and numerical analysis for resisitive magnetohydrodynamic operators" ICIA91,Abstracts. 102 (1991)

[Publications] Kojima Hisashi: "Remark on Belyi's paper concerning Galois extensions of the maximal cyclotomic field with certain linear groups as Galois groups" Tohoku Mathematical Journal. 43. 117-122 (1991)

[Publications] 長野 正,関口 次郎: "Commuting Involutions of Semisimple Groups" Tokyo Journal of Mathematics. 14. 319-327 (1991)

[Publications] 関口 次郎: "An Euler Type Integral Formula for Zonal Spherical Functions on SO。(m,2)/SO(m) SO(2)" Bulletin of the University of ElectroーCommunications. 4. 87-103 (1991)

[Publications] 小藤 俊幸: "指数2の微分ー代数系の数値解法における簡約Newton法" 情報処理学会論文誌. 32. 133-139 (1991)

[Publications] Koto T.: "ThirdーOrder SemiーImplicit RungeーKutta Methods for TimeーDependent IndexーOne DifferentialーAlgebraic Equations" J.of Information Processing. 14. 172-177 (1991)

[Publications] Nakamura M.: "On the Magnetic Benard Problew" J.Fac.Sci.Univ.Tokyo,Sec.IA. 38. 359-393 (1991)

[Publications] Nakamura M.: "On an Equilibrium of the Plasma in a Tokamak with Limiter" Japan J.of Ind.Appl.Math.8. 431-444 (1991)

[Publications] 花田 孝郎,今井 仁司,河原田 秀夫,名取 亮: "凝固現象の数値解析" 数理解析研究所講究録「Phase transitionと最適制御」. (1992)

[Publications] 花田 孝郎,今井 仁司,河原田 秀夫,名取 亮: "体積変化と接触点の運動を考慮したステファン問題の数値解析" 応用数学合同シンポジウム(京都大学・数理解析研究所). (1991)

[Publications] Tabata M,Fujima S.: "Finiteーelement analysis of high Reynolds number flows past a circular cylinder" J.of Computational and Applied Mathematics. 38. 411-424 (1991)

[Publications] Kaizu S.: "The Poisson equation in domains with many tiny cracks" International Congress of Mathematicians,Abstracts,Short Communications,Kyoto,Japan,August. 168 (1991)

[Publications] Kaizu S.: "The Poisson equation with nonautonomous semilinear boundary conditions in domains with many tinyholes" SIAM J. Math. Anal.22. 1222-1245 (1991)

[Publications] 田端 正久(分担執筆): "現代数理科学辞典" 大阪書店, 1310(8) (1991)

梅津聰電気通信大学, 電気通信学部, 助教授 (80017409)

[Publications] 田端正久,小林俊雄: "自由境界問題のラグランジュ有限要素近似" 「自由境界問題の数値解析とその周辺」京都大学数理解析研究所講究録. 744. 15-28 (1991)

[Publications] 渡辺二郎: "石けん膜の安定性をめぐって" 応用数理. 2(1号). (1992)

[Publications] 長野正,関口次郎: "Commuting Involutions of Semisimple Groups" Tokyo Journal of Mathematics. 14. 319-327 (1991)

[Publications] 関口次郎: "An Euler Type Integral Formula for Zonal Spherical Functions on SO。(m,2)/SO(m) SO(2)" Bulletin of the University of ElectroーCommunications. 4. 87-103 (1991)

[Publications] 小藤俊幸: "指数2の微分ー代数系の数値解法における簡約Newton法" 情報処理学会論文誌. 32. 133-139 (1991)

[Publications] 花田孝郎,今井仁司,河原田秀夫,名取亮: "凝固現象の数値解析" 数理解析研究所講究録「Phase transitionと最適制御」. (1992)

[Publications] 花田孝郎,今井仁司,河原田秀夫,名取亮: "体積変化と接触点の運動を考慮したステファン問題の数値解析" 応用数学合同シンポジウム(京都大学・数理解析研究所). (1991)

[Publications] 田端正久(分担執筆): "現代数理科学辞典" 大阪書店, 1310(8) (1991)