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Volume 3, Issue 2
A Block Monotone Domain Decomposition Algorithm for a Nonlinear Singularly Perturbed Parabolic Problem

Igor Boglaev

Int. J. Numer. Anal. Mod., 3 (2006), pp. 211-231.

Published online: 2006-03

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  • Abstract

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on a block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each time level and converges monotonically to the exact solution of the nonlinear problem. The rate of convergence of the block monotone domain decomposition algorithm is estimated. Numerical experiments are presented.

  • Keywords

singularly perturbed parabolic problem, block monotone method, nonoverlapping domain decomposition, monotone Schwarz alternating algorithm.

  • AMS Subject Headings

65N06, 65N50, 65N55, 65H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-211, author = {Boglaev , Igor}, title = {A Block Monotone Domain Decomposition Algorithm for a Nonlinear Singularly Perturbed Parabolic Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {2}, pages = {211--231}, abstract = {

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on a block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each time level and converges monotonically to the exact solution of the nonlinear problem. The rate of convergence of the block monotone domain decomposition algorithm is estimated. Numerical experiments are presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/897.html} }
TY - JOUR T1 - A Block Monotone Domain Decomposition Algorithm for a Nonlinear Singularly Perturbed Parabolic Problem AU - Boglaev , Igor JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 211 EP - 231 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/897.html KW - singularly perturbed parabolic problem, block monotone method, nonoverlapping domain decomposition, monotone Schwarz alternating algorithm. AB -

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on a block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each time level and converges monotonically to the exact solution of the nonlinear problem. The rate of convergence of the block monotone domain decomposition algorithm is estimated. Numerical experiments are presented.

Boglaev , Igor. (2006). A Block Monotone Domain Decomposition Algorithm for a Nonlinear Singularly Perturbed Parabolic Problem. International Journal of Numerical Analysis and Modeling. 3 (2). 211-231. doi:
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