Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem. (English) Zbl 1003.65091
This paper gives maximum norm error estimates, uniform in the perturbation parameter, for variable step first- and second-order finite difference schemes when solving singularly perturbed quasi-linear two point boundary value problems with an exponential boundary layer. Numerical results are presented which confirm the theoretical analysis.
Reviewer: Kevin Burrage (Brisbane)
MSC:
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34E15 | Singular perturbations for ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
