一类半线性椭圆方程的二重网格差分算法

一类半线性椭圆方程的二重网格差分算法

刘伟¹,芮洪兴²

1. 鲁东大学数学与信息学院, 山东烟台 264025; 2. 山东大学数学与系统科学学院, 山东济南 250100

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 刘伟

A two-grid algorithm for a finite difference solution of semi-linear elliptic equations

LIU Wei¹, RUI Hong-xing²

1. School of Mathematics andInformation, Ludong University, Yantai 264025, Shandong, China;2. School of Mathematics and System Sciences, Shandong University, Jinan 250100, Shandong, China

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: LIU Wei

摘要/Abstract

摘要： 应用二重网格差分算法处理了一类半线性椭圆问题。无需求细网格上的非线性解,对粗网格(可以很粗)上的数值解在细网格上进行几次线性修正即可,且重复算法的最后一步可以按粗网格步长任意阶地逼近细网格上的非线性解。算法提高了计算效率但不降低精度,有数值算例加以验证。

关键词: 有限差分法, 二重网格法 , 半线性方程

Abstract: An efficient two-grid algorithm was presented for the approximation of semi-linear elliptic equations using the finite difference method. The solution of a nonlinear system in fine space was reduced to the solution of one small system in coarse space and two linear systems on the fine space. A remarkable fact is that any order accuracy of approximation in coarse grid size can be obtained if other iterations are performed similarly to last step of the algorithm. The numerical results confirm that the algorithm obtains a decrease in the amount of computing time without sacrificing the order of accuracy of the fine grid solution.

Key words: two-grid method , semilinear equations, finite difference method

中图分类号:

O241.3

刘伟,芮洪兴 . 一类半线性椭圆方程的二重网格差分算法[J]. J4, 2008, 43(4): 51-54 .

LIU Wei, RUI Hong-xing . A two-grid algorithm for a finite difference solution of semi-linear elliptic equations[J]. J4, 2008, 43(4): 51-54 .

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