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

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Uygulamalı Matematik Enstitüsü, Türkiye

Tezin Onay Tarihi: 2015

Öğrenci: SENEM AKTAŞ

Danışman: BÜLENT KARASÖZEN

Özet:

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.