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Monotone finite difference domain decomposition algorithms and applications to nonlinear singularly perturbed reaction-diffusion problems

Advances in Difference Equations volume 2006, Article number: 070325 (2006) Cite this article

Abstract

This paper deals with monotone finite difference iterative algorithms for solving nonlinear singularly perturbed reaction-diffusion problems of elliptic and parabolic types. Monotone domain decomposition algorithms based on a Schwarz alternating method and on box-domain decomposition are constructed. These monotone algorithms solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear discrete problems. The rate of convergence of the monotone domain decomposition algorithms are estimated. Numerical experiments are presented.

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Authors and Affiliations

  1. Institute of Fundamental Sciences, Massey University, Private Bag, Palmerston North 11-222, New Zealand

    Igor Boglaev & Matthew Hardy

Authors
  1. Igor Boglaev
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  2. Matthew Hardy
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Correspondence to Igor Boglaev.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Boglaev, I., Hardy, M. Monotone finite difference domain decomposition algorithms and applications to nonlinear singularly perturbed reaction-diffusion problems. Adv Differ Equ 2006, 070325 (2006). https://doi.org/10.1155/ADE/2006/70325

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  • DOI: https://doi.org/10.1155/ADE/2006/70325

Keywords

  • Differential Equation
  • Exact Solution
  • Partial Differential Equation
  • Numerical Experiment
  • Ordinary Differential Equation