期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 39, 期 2, 页码 647-667出版社
SIAM PUBLICATIONS
DOI: 10.1137/S0036142999361396
关键词
time-periodic solution; reaction-diffusion-convection equation; monotone iterations; finite difference equations; convergence; error estimates
This paper is devoted to a numerical analysis of periodic solutions of a finite difference system which is a discrete version of a class of nonlinear reaction-diffusion-convection equations under nonlinear boundary conditions. Three monotone iterative schemes for the finite difference system are presented, and it is shown by the method of upper and lower solutions that the sequence of iterations from each of these iterative schemes converges monotonically to either a maximal periodic solution or a minimal periodic solution depending on whether the initial iteration is an upper solution or a lower solution. A comparison theorem for the various monotone sequences is given. It is also shown that the maximal and minimal periodic solutions of the finite difference system converge to the corresponding maximal and minimal periodic solutions of the reaction-diffusion-convection equation as the mesh size decreases to zero. Some error estimates between the theoretical and the computed iterations for each of the three iterative schemes are obtained, and a discussion on the numerical stability of these schemes is given. Also given are some numerical results of a logistic reaction diffusion problem.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据