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Engineering with Computers
Erschienen in: Engineering with Computers 3/2021

18.01.2020 | Original Article

Numerical simulations for the predator-prey model on surfaces with lumped mass method

verfasst von: Meng Zhang, Xufeng Xiao, Xinlong Feng

Erschienen in: Engineering with Computers | Ausgabe 3/2021

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Abstract

The predator-prey model is powerful mathematical tool to describe the dynamics of biological systems and promote research on biological populations. In this paper, we present a lumped mass finite element method for solving the predator-prey models on surfaces. The main purpose of the proposed method is to overcome the difficulty of the positivity preservation of the solutions. Based on positivity preservation results, we investigate the stabilities of semi-discrete and fully discrete approximations. Besides, numerical simulations are considered to illustrate the feasibility of the numerical method by convergence tests. Two classical phenomena of the predator-prey model are simulated on three different implicit surfaces.
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Metadaten
Titel
Numerical simulations for the predator-prey model on surfaces with lumped mass method
verfasst von
Meng Zhang
Xufeng Xiao
Xinlong Feng
Publikationsdatum
18.01.2020
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 3/2021
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-019-00929-4

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