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Volume 31, Issue 6
Uniform Quadratic Convergence of a Monotone Weighted Average Method for Semilinear Singularly Perturbed Parabolic Problems

Igor Boglaev

DOI: 10.4208/jcm.1307-m4238

J. Comp. Math., 31 (2013), pp. 620-637.

Published online: 2013-12

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  • Abstract

This paper deals with a monotone weighted average iterative method 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 weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.

  • Keywords

Semilinear parabolic problem, Singular perturbation, Weighted average scheme, Monotone iterative method, Uniform convergence.

  • AMS Subject Headings

65M06, 65N06.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-31-620, author = {Igor Boglaev}, title = {Uniform Quadratic Convergence of a Monotone Weighted Average Method for Semilinear Singularly Perturbed Parabolic Problems}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {6}, pages = {620--637}, abstract = {

This paper deals with a monotone weighted average iterative method 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 weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1307-m4238}, url = {http://global-sci.org/intro/article_detail/jcm/9757.html} }
TY - JOUR T1 - Uniform Quadratic Convergence of a Monotone Weighted Average Method for Semilinear Singularly Perturbed Parabolic Problems AU - Igor Boglaev JO - Journal of Computational Mathematics VL - 6 SP - 620 EP - 637 PY - 2013 DA - 2013/12 SN - 31 DO - http://doi.org/10.4208/jcm.1307-m4238 UR - https://global-sci.org/intro/article_detail/jcm/9757.html KW - Semilinear parabolic problem, Singular perturbation, Weighted average scheme, Monotone iterative method, Uniform convergence. AB -

This paper deals with a monotone weighted average iterative method 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 weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.

Igor Boglaev. (2013). Uniform Quadratic Convergence of a Monotone Weighted Average Method for Semilinear Singularly Perturbed Parabolic Problems. Journal of Computational Mathematics. 31 (6). 620-637. doi:10.4208/jcm.1307-m4238
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