Numerical Solutions of Nonlinear Parabolic Problems by Monotone Jacobi and Gauss-Seidel Methods

Volume 8, Issue 4

I. Boglaev

DOI:

Int. J. Numer. Anal. Mod., 8 (2011), pp. 599-614

Published online: 2011-08

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Abstract

This paper is concerned with solving nonlinear monotone difference schemes of the parabolic type. The monotone Jacobi and monotone Gauss-Seidel methods are constructed. Convergence rates of the methods are compared and estimated. The proposed methods are applied to solving nonlinear singularly perturbed parabolic problems. Uniform convergence of the monotone methods is proved. Numerical experiments complement the theoretical results.

Keywords

Nonlinear parabolic problem monotone iterative method singularly perturbed problem uniform convergence

AMS Subject Headings

65M06 65H10 65F10

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@Article{IJNAM-8-599, author = {I. Boglaev}, title = {Numerical Solutions of Nonlinear Parabolic Problems by Monotone Jacobi and Gauss-Seidel Methods}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {4}, pages = {599--614}, abstract = {This paper is concerned with solving nonlinear monotone difference schemes of the parabolic type. The monotone Jacobi and monotone Gauss-Seidel methods are constructed. Convergence rates of the methods are compared and estimated. The proposed methods are applied to solving nonlinear singularly perturbed parabolic problems. Uniform convergence of the monotone methods is proved. Numerical experiments complement the theoretical results.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/703.html} }

TY - JOUR T1 - Numerical Solutions of Nonlinear Parabolic Problems by Monotone Jacobi and Gauss-Seidel Methods AU - I. Boglaev JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 599 EP - 614 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/703.html KW - Nonlinear parabolic problem KW - monotone iterative method KW - singularly perturbed problem KW - uniform convergence AB - This paper is concerned with solving nonlinear monotone difference schemes of the parabolic type. The monotone Jacobi and monotone Gauss-Seidel methods are constructed. Convergence rates of the methods are compared and estimated. The proposed methods are applied to solving nonlinear singularly perturbed parabolic problems. Uniform convergence of the monotone methods is proved. Numerical experiments complement the theoretical results.

I. Boglaev. (1970). Numerical Solutions of Nonlinear Parabolic Problems by Monotone Jacobi and Gauss-Seidel Methods. International Journal of Numerical Analysis and Modeling. 8 (4). 599-614. doi:

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