An Adaptive Uniformly Convergent Numerical Method for a Semilinear Singular Perturbation Problem

DOI10.1137/0726025zbMath0685.65075OpenAlexW1963712700MaRDI QIDQ4203742

Martin Stynes

Publication date: 1989

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/512d90a2e6b3f39c7a93c9b3f700e4ad4c0162a9

zbMATH Keywords

numerical examplesdifference schemeboundary layersnonuniform meshesadaptiveinterior layerssemilinear singular perturbation problemlocally quasi-uniform meshuniformly convergent numerical method

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Finite element analysis of exponentially fitted lumped schemes for time- dependent convection-diffusion problems ⋮ Finite element methods on piecewise equidistant meshes for interior turning point problems ⋮ Uniformly convergent NIPG method for singularly perturbed convection diffusion problem on Shishkin type meshes ⋮ A class of difference schemes uniformly convergent on a modified Bakhvalov mesh ⋮ High-order uniformly convergent method for nonlinear singularly perturbed delay differential equations with small shifts ⋮ Numerical exploration of a system of reaction-diffusion equations with internal and transient layers ⋮ A survey of numerical techniques for solving singularly perturbed ordinary differential equations

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