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A Legendre spectral element method on a large spatial domain to solve the predator-prey system modeling interacting populations. (English) Zbl 1352.65389

Summary: A Legendre spectral element method is developed for solving a one-dimensional predator-prey system on a large spatial domain. The predator-prey system is numerically solved where the prey population growth is described by a cubic polynomial and the predator’s functional response is Holling type I. The discretization error generated from this method is compared with the error obtained from the Legendre pseudospectral and finite element methods. The Legendre spectral element method is also presented where the predator response is Holling type II and the initial data are discontinuous.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
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