Numerical investigation of the population distribution in heterogenous domain

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Henry_Stephen_Thesis.pdf (9.92 MB)

Date

2023-08

Authors

Henry, Stephen Andre

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https://hdl.handle.net/1969.6/97721

Abstract

We consider the spatial-temporal model of multi-species population distribution in two-dimensional heterogeneous domains. A coupled system of time-dependent diffusion-reaction equations describes the mathematical model of such problems. To solve the problem numerically, we construct an unstructured grid that resolves inclusions on the grid level and produces a semi-discrete system using a finite element method. For time approximation, we apply an explicit-implicit scheme where the reaction term of the equation is taken from the previous time layer. We present numerical results for several test problems to investigate the influence of the geometry and parameters on time to reach equilibrium and the final equilibrium state. An extension of the model is also considered, where we add a memory effect by introducing a time-fractional multi-species model. We derive an implicit finite difference approximation for time discretization based on Caputo’s time fractional derivative. A numerical investigation is performed for various orders of the time derivative.

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A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics

Keywords

2D ellpitical parabolic ODE, finite element method, fractional derivatives, numerical simulations & results, partial differential equation

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