带非线性边界条件的反应扩散方程的数值方法  

NUMERICAL METHODS FOR REACTION-DIFFUSION EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

作　　者：邓卫兵[1] 陈玉娟[1] 

机构地区：[1]南京大学数学系,南京210093

出　　处：《高等学校计算数学学报》2000年第4期353-361,共9页Numerical Mathematics A Journal of Chinese Universities

摘　　要：In this paper we study the finite difference equations corresponding to a class of semilinear parabolic equations with nonlinear boundary conditions in a bounded domain. Using the method of upper-lower solutions we construct two monotone sequences for finite difference systems. It is shown that these two sequences converge monotonically from above and below, respectively, to a unique solution of the nonlinear discrete equations. Moreover, the monotone convergence property is used to prove the convergence of the finite difference solution to the corresponding solution of the differential system as the mesh size decreases to zero.In this paper we study the finite difference equations corresponding to a class of semilinear parabolic equations with nonlinear boundary conditions in a bounded domain. Using the method of upper-lower solutions we construct two monotone sequences for finite difference systems. It is shown that these two sequences converge monotonically from above and below, respectively, to a unique solution of the nonlinear discrete equations. Moreover, the monotone convergence property is used to prove the convergence of the finite difference solution to the corresponding solution of the differential system as the mesh size decreases to zero.

关 键 词：反应扩散方程 数值方法 非线性边界条件 非线性抛物型方程 

分 类 号：O241.82[理学—计算数学]