On modified accelerated monotone iterates for solving semilinear parabolic problems

Authors:
Igor Boglaev
Affiliations:
Institute of Fundamental Sciences, Massey University, Private Bag 11-222, Palmerston North, New Zealand
Venue:
Applied Numerical Mathematics
Year:
2012

Citing 4
Cited 0

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

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Abstract

This paper deals with numerical solutions of nonlinear parabolic problems. Monotone sequences, based on a modified accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates a nonlinear parabolic problem. The monotone convergence leads to the existence-uniqueness theorem. An analysis of a convergence rate of the modified accelerated monotone iterative method is given. Numerical experiments are presented.