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A Numerical Method for Multispecies Populations in a Moving Domain Using Combined Masses

Author

Listed:
  • M. J. Baines

    (Department of Mathematics and Statistics, University of Reading, Reading RG6 6AH, UK
    These authors contributed equally to this work.)

  • Katerina Christou

    (Department of Mathematics and Statistics, University of Reading, Reading RG6 6AH, UK
    These authors contributed equally to this work.)

Abstract

This paper concerns the numerical evolution of two interacting species satisfying coupled reaction–diffusion equations in one dimension which inhabit the same part of a moving domain. The domain has both moving external boundaries and moving interior interfaces where species may arise, overlap, or disappear. Numerically, a moving finite volume method is used in which node movement is generated by local mass preservation, which includes a general combined mass strategy for species occupying overlapping domains. The method is illustrated by a test case in which a range of parameters is explored.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1124-:d:785006
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    References listed on IDEAS

    as
    1. Guohong Zhang & Xiaoli Wang, 2014. "Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, June.
    2. 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.
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