A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with discontinuous data

DOI10.1016/j.amc.2006.01.094zbMath1109.65066OpenAlexW2040973668MaRDI QIDQ861102

Sophie Pack, Igor P. Boglaev

Publication date: 9 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.01.094

zbMATH Keywords

singular perturbationerror estimatesuniform convergencenumerical examplesupper and lower solutionsdiscontinuous datamonotone iterative methodboundary and interior layersnonlinear difference schemesemilinear reaction-diffusion problems

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) 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) 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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• Uniform numerical methods on arbitrary meshes for singularly perturbed problems with discontinuous data
• Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convec\-tion coefficient
• Approximate solution of a non-linear boundary value problem with a small parameter for the highest-order differential

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