Reduced Basis Approximation for a Spatial Lotka-Volterra Model

Abstract

We construct a reduced basis approximation for the solution to a system of nonlinear partial differential equations describing the temporal evolution of two populations following the Lotka-Volterra law. The first population’s carrying capacity contains a free parameter varying in a compact set. The reduced basis is constructed by two approaches: a proper orthogonal decomposition of a collection of solution snapshots and a greedy algorithm using an a posteriori error estimator.