Monotone iterations for numerical solutions of reaction-diffusion-convection equations with time delay
✍ Scribed by C. V. Pao
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 375 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0749-159X
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✦ Synopsis
In this article we use the monotone method for the computation of numerical solutions of a nonlinear reactiondiffusion-convection problem with time delay. Three monotone iteration processes for a suitably formulated finite-difference system of the problem are presented. It is shown that the sequence of iteration from each of these iterative schemes converges from either above or below to a unique solution of the finite-difference system without any monotone condition on the nonlinear reaction function. An analytical comparison result among the three processes of iterations is given. Also given is the application of the iterative schemes to some model problems in population dynamics, including numerical results of a model problem with known analytical solution.