Numerical solutions of Gelfand equation in steady combustion process
发布时间：2023-02-16
点击次数：
发表刊物：Applied Mathematics and Computation
摘要：In this paper, we study a numerical algorithm to find all solutions of Gelfand equation. By utilizing finite difference discretization, the model problem defined on bounded do- main with Dirichlet condition is converted to a nonlinear algebraic system, which is solved by cascadic multigrid method combining with Newton iteration method. The key of our numerical method contains two parts: a good initial guess which is constructed via col- location technique, and the Newton iteration step is implemented in cascadic multigrid method. Numerical simulations for both one-dimensional and two-dimensional Gelfand equations are carried out which demonstrate the effectiveness of the proposed algorithm. We find that by using the symmetry property of equation, numerical solutions can be obtained by mirror reflection after solving model problem in a sub-domain. This will save considerable time consumption and storage cost in computational process of cascadic multigrid method.
第一作者：Ruixue Sun
论文类型：期刊论文
通讯作者：Y. Xu
学科门类：理学
一级学科：数学
文献类型：J
卷号：441
页面范围：1-12
是否译文：否
发表时间：2022-10-28
收录刊物：SCI