GRID APPROXIMATION OF SINGULARLY PERTURBED PARABOLIC REACTION‐DIFFUSION EQUATIONS WITH PIECEWISE SMOOTH INITIAL‐BOUNDARY CONDITIONS

DOI10.3846/1392-6292.2007.12.235-254zbMath1139.65065OpenAlexW1985037001MaRDI QIDQ5457488

G. I. Shishkin

Publication date: 14 April 2008

Published in: Mathematical Modelling and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3846/1392-6292.2007.12.235-254

zbMATH Keywords

Dirichlet problemsingular perturbation\(\varepsilon\)-uniform convergenceboundary layerfinite differencecompatibility conditionsinterior layerparabolic reaction-diffusion equationspecial gridspiecewise smooth initial-boundary conditions

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) 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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (5)

Interior Layers in Singularly Perturbed Problems ⋮ A review on singularly perturbed differential equations with turning points and interior layers ⋮ Improved Difference Scheme for a Singularly Perturbed Parabolic Reaction-Diffusion Equation with Discontinuous Initial Condition ⋮ Singularly perturbed reaction-diffusion problems with discontinuities in the initial and/or the boundary data ⋮ Grid approximation of singularly perturbed parabolic equations with piecewise continuous initial-boundary conditions

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