Numerical solution of a quasi-linear parabolic equation with a boundary layer. (Russian) Zbl 0705.65067
A finite difference approximation to a singularly perturbed 1-D parabolic equation is constructed and studied. The nonlinear scheme is based on the method of lines and uses the technique of the exact difference schemes in space direction. The construction uses a special nonuniform grid, locally refined in the subdomain of the boundary layer, so that the convergence is uniform with respect to the small parameter. At the end, an interesting application of this approach for construction and study of difference approximation to a parabolic equation with boundary layer and moving boundary is given.
Reviewer: R.D.Lazarov
MSC:
65M20 | Method of lines 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 |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
35R35 | Free boundary problems for PDEs |
35K55 | Nonlinear parabolic equations |
35B25 | Singular perturbations in context of PDEs |