Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems

Authors:
Igor Boglaev
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 4
Cited 1

Numerical estimates for semilinear parabolic equations

SIAM Journal on Numerical Analysis
Monotone iterative algorithms for a nonlinear singularly perturbed parabolic problem

Journal of Computational and Applied Mathematics
Uniform convergence of a weighted average scheme for a nonlinear reaction-diffusion problem

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Higher-order monotone iterative methods for finite difference systems of nonlinear reaction--diffusion--convection equations

Applied Numerical Mathematics

Uniform quadratic convergence of monotone iterates for nonlinear singularly perturbed parabolic problems

Numerical Algorithms

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Abstract

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.