A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers

DOI10.1016/S0377-0427(99)00380-5zbMath1010.65031MaRDI QIDQ5937189

H. MacMullen, John J. H. Miller, Eugene O'Riordan, G. I. Shishkin

Publication date: 22 May 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergencesingular perturbationnumerical experimentserror boundsreaction-diffusion problemsboundary layersfinite differencediscrete Schwarz method

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12)

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Cites Work

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• On a domain decomposition algorithm for a singularly perturbed reaction-diffusion problem
• Computational method for a singular perturbation problem via domain decomposition and its parallel implementation
• A Uniformly Accurate Finite-Element Method for a Singularly Perturbed One-Dimensional Reaction-Diffusion Problem
• Uniform Convergence of the Schwarz Alternating Method for Solving Singularly Perturbed Advection-Diffusion Equations
• On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems
• Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
• Heterogeneous Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems
• FACTORIZATION OF THE CONVECTION-DIFFUSION OPERATOR AND THE SCHWARZ ALGORITHM
• A Schwarz Alternating Procedure for Singular Perturbation Problems

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