Higher-order time accurate numerical methods for singularly perturbed parabolic partial differential equations

DOI10.1080/00207160701798764zbMath1169.65083OpenAlexW2126929078MaRDI QIDQ5190725

Srinivasan Natesan, Rajdeep Deb

Publication date: 27 July 2009

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160701798764

zbMATH Keywords

singular perturbationnumerical examplesCrank-Nicolson schemereaction-diffusion equationcubic splineinitial-boundary-value problemspiecewise-uniform Shishkin meshextended-trapezoidal scheme

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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (8)

Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems ⋮ A robust numerical scheme for singularly perturbed parabolic reaction-diffusion problems via the method of lines ⋮ Trigonometric B-spline based ε-uniform scheme for singularly perturbed problems with Robin boundary conditions ⋮ Application of sinc-Galerkin method to singularly perturbed parabolic convection-diffusion problems ⋮ Richardson extrapolation technique for singularly perturbed parabolic convection--diffusion problems ⋮ A quintic spline collocation method for solving time-dependent convection-diffusion problems ⋮ A nonstandard fitted operator method for singularly perturbed parabolic reaction-diffusion problems with a large time delay ⋮ Shishkin mesh based septic Hermite interpolation algorithm for time-dependent singularly perturbed convection-diffusion models

Cites Work

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• Uniformly convergent difference schemes for singularly perturbed parabolic diffusion-convection problems without turning points
• Finite element analysis of exponentially fitted lumped schemes for time- dependent convection-diffusion problems
• An extended trapezoidal formula for the diffusion equation

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