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A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion

Author

Listed:
  • Michael John Baines

    (Department of Mathematics and Statistics, School of Mathematical, Physical and Computational Sciences (SMPCS), Faculty of Science, University of Reading, Reading RG6 6AH, UK
    These authors contributed equally to this work.)

  • Katerina Christou

    (Department of Mathematics and Statistics, School of Mathematical, Physical and Computational Sciences (SMPCS), Faculty of Science, University of Reading, Reading RG6 6AH, UK
    These authors contributed equally to this work.)

Abstract

A moving-mesh finite-difference solution of a Lotka-Volterra competition-diffusion model of theoretical ecology is described in which the competition is sufficiently strong to spatially segregate the two populations, leading to a two-phase problem with a coupling condition at the moving interface. A moving mesh approach preserves the identities of the two species in space and time, so that the parameters always refer to the correct population. The model is implemented numerically with a variety of parameter combinations, illustrating how the populations may evolve in time.

Suggested Citation

  • Michael John Baines & Katerina Christou, 2021. "A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:386-:d:499761
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    Cited by:

    1. M. J. Baines & Katerina Christou, 2022. "A Numerical Method for Multispecies Populations in a Moving Domain Using Combined Masses," Mathematics, MDPI, vol. 10(7), pages 1-17, April.

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