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数式処理による微分方程式の研究

通过数学公式处理研究微分方程

基本信息

批准号：
08640220
负责人：
河野實彦
金额：
$ 1.34万
依托单位：
Kumamoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至无数据
项目状态：
已结题

项目摘要

研究代表者の主たる研究目的は、多変数複素領域における完全積分可能な偏微分方程式系の大域的解析にある。モノドロミ-群、基本解間の接続問題、または不確定特異点にあってはストークス現象等の解明であるが、こうした大域的研究は未だ十分に解明されたとは言えない。多変数超幾何関数やその合流形に関しては、近年代数学や幾何学的考察、特に群論的観察によって非常に面白い結果が挙がりつつある。この方面には研究分担者木村、原岡も大いに貢献した所である。さて、微分方程式の研究においても複雑で厄介な計算が介在する。モノドロミ-群の計算やセクション上における微分方程式の導出、特異点におけるブロ-アップによる変形の繰返し等は数式処理によるエキスパートシステムを構築して、対処したいものである。この方面に関して、研究代表者は数々の結果を得ているが、本研究課題遂行中は、そうした微分方程式における数式処理に関する本を二冊まとめた。「微分方程式入門」(既刊)はそうした観点からまとめた本格的な入門書であるが、「微分方程式と数式処理」には、これまでの成果と共に新たな考察も加えてある。また、未刊の「Global Analysis in Linear Differential Equations」にも加筆した。これは、IP_1上の微分方程式に対する大域的理論をまとめたものである。

The representative of the research is "the purpose of the research", the number of complex elements in the field of complete positive analysis of partial differential equations may be the analytical solution of the large domain. The research on how to solve the problem of interconnection between basic solutions, such as the problem of basic solution, the problem of connection between basic solutions, the problem of connection between basic solutions, the problem of connection between basic solutions, the problem of connection between basic solutions, and so on, has not been fully understood. The results of the study of the manifold, the investigation of the study of mathematics in recent years, and the results of the special group theory show that the results are very clear. In the aspect of the study, Kimura, who is responsible for the study, is responsible for the study of the participants in the study. In the study of differential equations, the calculation of non-linear equations and differential equations is very important. The differential equation is derived from the differential equation derived from the differential equation, the special point is derived from the differential equation, the special point is derived from the differential equation, the differential equation is derived from the differential equation, the special point is derived from the differential equation, the special point is derived from the differential equation, the differential equation is derived from the differential equation, the differential equation is derived from the differential equation derived from the differential equation, the special point is derived from the differential equation, and so on. In this study, the differential equation is used to calculate the differential equation, and the mathematical formula is used in this study. in this study, the differential equation is used in this study. The introduction of differential equations (the current issue), the introduction of differential equations, and the results of differential equations. Do not publish the word "Global Analysis in Linear Differential Equations" and add others to the list. The theory of differential equations on the IP_1 and the theory of the whole field.