Numerical solutions for some coupled systems of nonlinear boundary value problems |
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Authors: | C. V. Pao |
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Affiliation: | (1) Department of Mathematics, North Carolina State University, P.O. Box 8205, 27695-8205 Raleigh, NC, USA |
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Abstract: | Summary In the well-known Volterra-Lotka model concerning two competing species with diffusion, the densities of the species are governed by a coupled system of reaction diffusion equations. The aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems. This iterative scheme is based on the method of upper-lower solutions which leads to two monotone sequences from some uncoupled linear systems. It is shown that each of the two sequences converges to a nontrivial solution of the discrete equations. The model under consideration may have one, two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration. Numerical results are given for these solutions under both the Dirichlet boundary condition and the mixed type boundary condition. |
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Keywords: | AMS(MOS): 65N20 CR: G1.8 |
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