A Finite Difference Approximation for a Coupled System of Nonlinear Size-Structured Populations
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
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We study a quasilinear nonlocal hyperbolic initial-boundary value problem that models the evolution of N size-structured subpopulations competing for common resources. We develop an implicit finite difference scheme to approximate the solution of this model. The convergence of this approximation to a unique bounded variation weak solution is obtained. The numerical results for a special case of this model suggest that when subpopulations are closed under reproduction, one subpopulation survives and the others go to extinction. Moreover, in the case of open reproduction, survival of more than one population is possible.
- Numerical Mathematics
- Theoretical Mathematics