High order \(\varepsilon\)-uniform methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and singular sources. (English) Zbl 1032.65090
A one-dimensional reaction-diffusion equation with discontinuous coefficients and singular sources is considered. For the solution of this problem some \(\varepsilon\)-uniformly convergent monotone finite difference schemes of second, third and fourth order on Shishkin meshes are constructed. Numerical examples are presented and discussed.
Reviewer: Boško Jovanović (Beograd)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 35K57 | Reaction-diffusion equations |
