Stability of difference equations generated by parabolic differential functional equations. (English) Zbl 1073.65087
From the abstract: The aim of this paper is to present a numerical approximation for the initial boundary value problem for quasilinear parabolic differential functional equations. The convergence result is proved for the difference scheme with the property that the difference operators approximating the mixed derivatives depend on local properties of the coefficients of the differential equation. A numerical example is given.
Reviewer: Nguyen Van Minh (Carrollton)
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 |
| 35K55 | Nonlinear parabolic equations |
| 35R10 | Partial functional-differential equations |
| 39A11 | Stability of difference equations (MSC2000) |
