An unconditionally stable numerical scheme for competing species undergoing nonlocal dispersion

Jianlong Han; Seth Armstrong; Sarah Duffin; Jianlong Han; Seth Armstrong; Sarah Duffin

doi:10.3934/era.2024114

Electronic Research Archive

2024, Volume 32, Issue 4: 2478-2490. doi: 10.3934/era.2024114

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An unconditionally stable numerical scheme for competing species undergoing nonlocal dispersion

Department of Mathematics, Southern Utah University, 351 W University Blvd, Cedar City, UT 84720, USA

Received: 01 January 2024 Revised: 04 March 2024 Accepted: 12 March 2024 Published: 26 March 2024

Nonstandard numerical approximation for the study of a competition model for two species that experience nonlocal diffusion, or dispersion, allows for faithful representation of the theoretical solution to the system. Such a scheme may preserve positivity of solutions, be uniquely solvable, and be completely stable. Under appropriate conditions, the error between the scheme and the theoretical solution can be measured. We present such a scheme here and confirm its desirable properties as they reflect the solution to the system.
- finite difference scheme,
- convergence,
- nonstandard scheme,
- competition model,
- population dynamics
Citation: Jianlong Han, Seth Armstrong, Sarah Duffin. An unconditionally stable numerical scheme for competing species undergoing nonlocal dispersion[J]. Electronic Research Archive, 2024, 32(4): 2478-2490. doi: 10.3934/era.2024114

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Abstract

Nonstandard numerical approximation for the study of a competition model for two species that experience nonlocal diffusion, or dispersion, allows for faithful representation of the theoretical solution to the system. Such a scheme may preserve positivity of solutions, be uniquely solvable, and be completely stable. Under appropriate conditions, the error between the scheme and the theoretical solution can be measured. We present such a scheme here and confirm its desirable properties as they reflect the solution to the system.

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