Correction method and extrapolation method for singular two-point boundary value problems

被引：7
|
作者：
Guoqiang, Han [1 ]
Jiong, Wang [2 ]
Hayami, Ken [3 ]
Yuesheng, Xu [4 ]
机构：
[1] Department of Computer Science, South China University of Technology, Guangzhou, Guangdong Province, China
[2] Dept. of Comp. and Electron. Eng., Guangdong Prov. Inst. Tech. Person, Guangzhou, Guangdong Province, China
[3] Dept. of Mathematical Engineering, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku Tokyo 113-8656, Japan
[4] Department of Mathematics, North Dakota State University, Fargo, ND 58105, United States
来源：
| 2000年 / Elsevier Science B.V., Amsterdam, Netherlands卷 / 126期
关键词：
Approximation theory - Extrapolation - Finite difference method - Problem solving;
D O I：
10.1016/S0377-0427(99)00349-0
中图分类号：
O24 [计算数学];
学科分类号：
070102 ;
摘要：
In this paper, we first discuss the constructions of three-point finite-difference approximation and a spline approximation for a class of singular two-point boundary value problems: x-α(xαu′)′ = f(x,u),u′(0+) = 0, u(1) = A, α≥1. The asymptotic error expansions of the numerical solutions of these problems are obtained. From these asymptotic error expansions we find that the finite-difference solution and the spline approximation solution approximate the exact solution from two sides. So we can obtain correct solution of high-order accuracy. Richardson's extrapolation can also be done and the accuracy of numerical solution can be improved greatly. We also present numerical examples which show the performance and efficiency of our methods.
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