%0 Journal Article
%T THE IMPLICIT DIFFERENCE SCHEME FOR THE NONLINEAR  PARABOLIC EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS<br>带非局部边界条件的非线性抛物方程的隐式差分解法
%A Wan Zhengsu
%A <br>万正苏
%A 陈光南
%J 计算数学
%D 2008
%I 
%X Parabolic equations with nonlocal boundary conditions arise from quasi-static elasticity, electrochemistry and etc. In this paper, we construct an implicit finite difference scheme for the nonlinear parabolic equation with nonlocal boundary conditions. Moreover, using the discrete functional analysis and the fixed-point theorem, we prove that the numerical solution is exist and convergent  with the convergence order $O(\tau +h^2)$ in the $L_{\infty}$-norm. Numerical examples are given to illustrate the theoretical results.
%K nonlocal boundary condition
%K nonlinear parabolic equation
%K implicit difference scheme
%K convergence<br>非局部边界条件
%K 非线性抛物方程
%K 隐式差分格式
%K 收敛性
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=CC77F3CEF526D9CF0B3021650FB4E57E&aid=09D5340B9D015522B774C73D569FA4EB&yid=67289AFF6305E306&vid=340AC2BF8E7AB4FD&iid=E158A972A605785F&sid=84A93BA251D28205&eid=D1D63D047E37A053&journal_id=0254-7791&journal_name=计算数学&referenced_num=0&reference_num=12