Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:A4L-A
Session:
Number:A4L-A2
Guaranteed error estimate for solutions to two-point boundary value problems
Akitoshi Takayasu, Shin’ichi Oishi, Takayuki Kubo,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
We consider the ‘guaranteed’ error estimate for solutions to two-point boundary value problems. ‘Guaranteed error’ requires every error in solving the system. It is important and difficult to analyze the error which is caused by the truncation or the discretization of problems. We overcome these difficulties by using Newton-Kantorovich theorem and the solution operator to linearized problem. The original problem is transformed into a nonlinear operator equation. The guaranteed error is bounded by Newton-Kantorovich theorem through verifying some constants concerning the solution operator. Finally, numerical result is presented.