Improved Difference Scheme for a Singularly Perturbed Parabolic Reaction-Diffusion Equation with Discontinuous Initial Condition

DOI10.1007/978-3-642-00464-3_11zbMath1233.65060OpenAlexW1570935645MaRDI QIDQ3615648

G. I. Shishkin

Publication date: 24 March 2009

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-00464-3_11

zbMATH Keywords

convergenceDirichlet problemRichardson methodfinite difference schemepiecewise-uniform meshesadditive splitting of singularitiespiecewise-continuous initial conditionsingularly perturbed parabolic reaction-diffusion equation

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)

Cites Work

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• Approximation of the solutions and diffusion flows of singularly perturbed boundary-value problems with discontinuous initial conditions
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• Approximation of the solution and its derivative for the singularly perturbed Black-Scholes equation with nonsmooth initial data
• GRID APPROXIMATION OF SINGULARLY PERTURBED PARABOLIC REACTION‐DIFFUSION EQUATIONS WITH PIECEWISE SMOOTH INITIAL‐BOUNDARY CONDITIONS