オイラー法による微分方程式の近似解の誤差評価について

Material type: 文書・図像類

Author: 樋口, 功

Publisher: 愛知工業大学

Publication date: 2003-03-31

Material Format: Digital

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Note (General)：: By the fundamental theorem of Cauchy-Lipschitz , the existence and the uniqueness of the solution of the following initial value problem are assured: ...

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Material Type: 文書・図像類
Title: オイラー法による微分方程式の近似解の誤差評価について
Author/Editor: 樋口, 功
Author Heading: 樋口, 功
Publication, Distribution, etc.: 愛知工業大学
Publication Date: 2003-03-31
Publication Date (W3CDTF): 2003-03-31
Alternative Title: On the error estimation of the approximate solution of differential equation by Euler's method
Periodical title: 愛知工業大学研究報告. A, 基礎教育センター論文集 = Bulletin of Aichi Institute of Technology. Part A
No. or year of volume/issue: 38
Volume: 38
Pages: 13-19
ISSN (Periodical Title): ISSN : 0387-0804
Text Language Code: jpn
Target Audience: 一般
Note (General): By the fundamental theorem of Cauchy-Lipschitz , the existence and the uniqueness of the solution of the following initial value problem are assured: (dy)/(dx)=f(x,y), y(x_0)=y_0 . But we can not obtain the concrete form of the solution by the above fundamental theorem. In some elementary cases, the solution-function can be derived by simple calculations. But in many cases, the solution-function can not be obtained in general. So we need to have their approximate solutions instead of their true solutions with the help of computer. As the methods of finding the approximate solution, the Euler, the Heun and the Runge-Kutta methods are well known. In the present paper, we shall give the error estimation of approximate solution obtained by Euler's method when f(x,y) is Lipschitz continuous.
identifier:http://repository.aitech.ac.jp/dspace/handle/11133/2036
Access Restrictions: 限定公開
Periodical Title (NCID): AA11564921
https://ci.nii.ac.jp/ncid/AA11564921
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 愛知工業大学 : 愛知工業大学学術情報リポジトリ