Numerical verification methods of solutions for nonlinear singularly perturbed problem

概要

論文の詳細を見る
Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」In order to verify the solution of nonlinear boundary value problems by Nakao's computer-assisted numerical method on computer, it is required to find a constant, as sharp as possible, in the a priori error estimates for the finite element approximation of some simple linear problems. For singularly perturbed a bad effect on the a priori error estimates, i.e., leads to a large constant, if we use the usual approximation methods. In this paper, we propose some verification algorithms of solutions for nonlinear singularly perturbed problems by using the constant obtained in the a priori error estimates based on the exponential fitting method with Green's function. Some numerical examples which confirm us the effectiveness of our method are presented.