Stability of a nonlocal two-dimensional finite-difference problem. (English. Russian original) Zbl 1004.65091
Differ. Equ. 37, No. 7, 970-978 (2001); translation from Differ. Uravn. 37, No. 7, 926-932 (2001).
The authors consider a two-dimensional problem for the heat equation with boundary conditions of the first kind with respect to one of the space variables and nonlocal conditions with respect to the other variable. For an explicit finite difference scheme, they obtain a criterion for stability with respect to the initial data in a specially constructed energy norm.
Reviewer: Ziwen Jiang (Shandong)
MSC:
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
