Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Boglaev, Igor

关键词: Semilinear parabolic problem;    Singular perturbation;    Monotone iterative method;    Uniform convergence;   

DOI  :  10.1016/j.cam.2011.02.009

来源: Elsevier

【 摘 要 】

This paper deals with discrete monotone iterative methods for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated 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 iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented. (C) 2011 Elsevier B.V. All rights reserved.

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