HODIE finite difference schemes on generalized Shishkin meshes.

DOI10.1016/S0377-0427(03)00653-8zbMath1046.65064MaRDI QIDQ1426768

José Luis Gracia, Carmelo Clavero

Publication date: 15 March 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergencesingular perturbationnumerical examplesgenerating functionboundary layerShishkin meshuniformHODIE finite difference schemeslinear diffusion-convection problems

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (6)

High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Optimal error estimate of upwind scheme on Shishkin-type meshes for singularly perturbed parabolic problems with discontinuous convection coefficients ⋮ Analysis of a higher order uniformly convergent method for singularly perturbed parabolic delay problems ⋮ Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems ⋮ A parameter uniform higher order scheme for 2D singularly perturbed parabolic convection-diffusion problem with turning point

Cites Work

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• A study of difference schemes with the first derivative approximated by a central difference ratio
• A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems
• The midpoint upwind scheme
• A hybrid difference scheme on a Shishkin mesh for linear convection-diffusion problems
• An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
• High order methods on Shishkin meshes for singular perturbation problems of convection-diffusion type
• An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems
• Defect correction on Shishkin-type meshes

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