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  • Research Article
  • Open Access

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

Advances in Difference Equations20062006:070325

  • Received: 16 September 2004
  • Accepted: 11 January 2005
  • Published:


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.


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


Authors’ Affiliations

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


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© Boglaev and Hardy 2006

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