Difference scheme for a parabolic problem with changing time direction. (English. Russian original) Zbl 0841.65074
Lith. Math. J. 35, No. 1, 30-41 (1995); translation from Liet. Mat. Rink. 35, No. 1, 37-51 (1995).
The paper is devoted to construction and theoretical study of finite difference schemes for forward-backward parabolic equations of the type \(v(x)u_t = Lu + f\) in \((-1,1) \times (0,T)\), where \(L\) is a symmetric elliptic operator and \(v(x)\) is positive for \(x > 0\) and negative for \(x < 0\). The solution is subject to stable initial-boundary conditions. The stability of the constructed scheme is studied using maximum principle. The convergence for smooth solutions is proven in discrete energy norm. An iterative method for the linear system is proposed and studied.
Reviewer: R.R.D.Lazarov (College Station)
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 |
| 35K15 | Initial value problems for second-order parabolic equations |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
finite difference schemes; forward-backward parabolic equations; stability; convergence; iterative methodReferences:
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