Numerical simulation of advective Lotka-Volterra systems by discontinuous Galerkin method

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Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Turkey

Approval Date: 2015

Student: SENEM AKTAŞ

Supervisor: BÜLENT KARASÖZEN

Abstract:

In this thesis, we study numerically advection-diffusion-reaction equations arising from Lotka-Volterra models in river ecosystems characterized by unidirectional flow. We consider two and three species models which include competition, coexistence and extinction depending on the parameters. The one dimensional models are discretized by interior penalty discontinuous Galerkin model in space. For time discretization, fully implicit backward Euler method and semi-implicit IMEX-BDF methods are used. Numerical simulations for various set up parameters reveal more insight in the complicated dynamics by advective Lotka-Volterra systems.