Difference Methods for Singular Perturbation Problems

DOI10.1201/9780203492413zbMath1163.65062OpenAlexW577555718MaRDI QIDQ3525841

G. I. Shishkin, L. P. Shishkina

Publication date: 18 September 2008

Full work available at URL: https://doi.org/10.1201/9780203492413

zbMATH Keywords

monographsingular perturbationuniform convergencefinite difference schemesdefect correction methoddomain decomposition methodRichardson extrapolation methodboundary and interior layersparabolic reaction-diffusion problemsparabolic convection-diffusion problemspiecewise-uniform meshesconditioning of difference schemesdomains with smooth and piecewise-smooth boundarieselliptic convection-diffusion problemselliptic reaction-diffusion problemsmoving boundary layerssystems of elliptic problems

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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