Monotone and economical difference schemes on nonuniform grids for a multidimensional parabolic equation with a boundary condition of the third kind. (English) Zbl 1064.65096
Monotone conservative difference schemes of the second order of local approximation in space for a differential problem with boundary conditions of the third kind on arbitrary nonuniform grids in both time and space are constructed. For the multidimensional parabolic equation, monotone local one-dimensional difference schemes of the second order of local approximation in space on the minimal stencil are proposed. A priori estimates in the norm \(C\) are obtained on nonuniform grids by means of the grid maximum principle. Two numerical experiments are presented.
Reviewer: Pavol Chocholatý (Bratislava)
MSC:
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
65M15 | Error bounds 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 |
35K05 | Heat equation |