Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems |
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Authors: | Igor Boglaev |
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Institution: | Institute of Fundamental Sciences, Massey University, Private Bag 11-222, Palmerston North, New Zealand |
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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. |
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Keywords: | Semilinear parabolic problem Singular perturbation Monotone iterative method Uniform convergence |
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