ISSN:
0945-3245
Keywords:
AMS(MOS): 65N20
;
CR: G1.8
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01397542
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