UNIFORM QUADRATIC CONVERGENCE OF A MONOTONE WEIGHTED AVERAGE METHOD FOR SEMILINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS＊  

作　　者：Igor Bogluev 

机构地区：[1]Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand

出　　处：《Journal of Computational Mathematics》2013年第6期620-637,共18页计算数学（英文）

摘　　要：This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the ac- celerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the ac- celerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.

关 键 词：Semilinear parabolic problem Singular perturbation Weighted average scheme Monotone iterative method Uniform convergence. 

分 类 号：O174.21[理学—数学] F275[理学—基础数学]