求解带非线性边界条件的反应扩散方程数值解的组合迭代方法  

COMBINED ITERATIVE METHODS FOR NUMERICAL SOLUTION OF REACTION-DIFFUSION EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

作　　者：邓卫兵[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》2001年第2期111-120,共10页Numerical Mathematics A Journal of Chinese Universities

摘　　要：In this paper we study the monotone iterative schemes for numerical solution of the finite difference systems of semilinear parabolic equations with nonlinear boundary conditions. Two modified iterative schemes by combing the method of upper lower solutions and the Jacobi method or the Gauss Seidel method are presented. The convergence of the monotone iterative schemes is proved as well as the finite difference system converges to the continuous parabolic equations. In the end of this paper we give an error estimate to show that the two iterative methods are numerically stable.In this paper we study the monotone iterative schemes for numerical solution of the finite difference systems of semilinear parabolic equations with nonlinear boundary conditions. Two modified iterative schemes by combing the method of upper lower solutions and the Jacobi method or the Gauss Seidel method are presented. The convergence of the monotone iterative schemes is proved as well as the finite difference system converges to the continuous parabolic equations. In the end of this paper we give an error estimate to show that the two iterative methods are numerically stable.

关 键 词：非线性边界条件 组合迭代方法 上-下解 数值解 反应扩散方程 离散系统 误差估计 稳定性 

分 类 号：O241.81[理学—计算数学]