In this paper, we establish error bound analysis for a finite-difference approximation to the solutions for a class of Nonlinear Parabolic Systems in the form Ž . Ž . Ž . Ž . Ž . Ž . Ž . ѨrѨt ¨q ѨrѨx f ¨q ѨrѨ y g ¨q ѨrѨz h ¨s D ⌬¨. We assume that the initial data is sufficiently smooth and of class
A class of convergent finite difference schemes for certain nonlinear parabolic systems
✍ Scribed by Takaaki Nishida; Joel Smoller
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 730 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0010-3640
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## Abstract A linearized three‐level difference scheme on nonuniform meshes is derived by the method of the reduction of order for the Neumann boundary value problem of a nonlinear parabolic system. It is proved that the difference scheme is uniquely solvable and second‐order convergent in __L__~__
This article is a continuation of the work [M. Feistauer et al., Num Methods PDEs 13 (1997), 163-190] devoted to the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Non