A MONOTONE DOMAIN DECOMPOSITION ALGORITHM FOR SOLVING WEIGHTED AVERAGE APPROXIMATIONS TO NONLINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS  

作　　者：Igor Boglaev Matthew Hardy 

机构地区：[1]Institute of Fundamental Sciences,Massey University,Private Bag 11-222,Palmerston North,New Zealand [2]Mathematical Sciences Institute,Australian National University,Canberra,Australia 0200

出　　处：《Journal of Computational Mathematics》2008年第1期76-97,共22页计算数学（英文）

摘　　要：This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented.This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented.

关 键 词：Parabolic reaction-diffusion problem Boundary layers O-method Monotone domain decomposition algorithm Uniform convergence 

分 类 号：O175.29[理学—数学]