Reduced Basis Approximation for a Spatial Lotka-Volterra Model

Peter Rashkov
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Peter Rashkov: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, ul. Akademik Georgi Bonchev, Blok 8, 1113 Sofia, Bulgaria

Mathematics, 2022, vol. 10, issue 12, 1-12

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.

Keywords: reduced basis method; nonlinear reaction-diffusion equation; parametrised partial differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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