On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution

Journal of Computational and Applied Mathematics

Volumn 131, Issue 1-2, 2001, Pages 381-405

  Beckett, G ^a   Mackenzie, J A ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Adaptivity; Equidistribution; Reaction diffusion; Singular perturbation; Uniform convergence

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; FUNCTIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

FINITE DIFFERENCE APPROXIMATION;

DIFFUSION;

FINITE DIFFERENCE TECHNIQUE; MATHEMATICAL METHOD; REACTION-DIFFUSION EQUATION;

EID: 0035361441     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00260-0     Document Type: Article

References (31)

1. A posteriori error estimates for the finite element method
2. On the optimization of methods for solving boundary value problems with boundary layers
3. Convergence analysis of finite difference approximations on equidistributed grids for a singularly perturbed boundary value problem
4. On simple moving grid methods for one-dimensional evolutionary partial differential equations
5. Numerical solution of boundary value problems using nonuniform grids
6. Grading functions and mesh redistribution
7. Superconvergent grids for two-point boundary value problems
8. A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes
9. Good approximation by splines with variables knots II
10. Graded-mesh difference schemes for singularly perturbed two-point boundary value problems
11. A simple adaptive grid method in two dimensions
12. Moving mesh PDEs based on the equidistribution principle
13. The efficient generation of simple two-dimensional adaptive grids
14. Uniform convergence analysis of an upwind finite-difference approximation ofa convection-diffusion boundary value problem on an adaptive grid
15. Solution of evolutionary partial differential equations using adaptive finite differences with pseudospectral post-processing
16. A uniformly accurate finite element method for a singularly perturbed one-dimensional reaction-diffusion problem
17. Mesh selection for discrete solution of boundary problems in ordinary differential equations
18. On the convergence of iterated remeshing
19. Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
20. A posteriori error estimates for the finite element solution of a singularly perturbed linear ordinary differential equation
21. Global uniformly convergent schemes for a singularly perturbed boundary value problem using patched base spline-function
22. Adaptive mesh selection strategies for boundary value problems
23. Difference schemes for singularly perturbed parabolic equation with discontinuous boundary condition
24. Non-equidistant generalizations of the Gushchin-Schennikov scheme
25. On selection of equidistributing meshes for two-point boundary-value problems