Numerical solution of the Fisher’s equation with discontinous Galerkin method

Download
2015
Özsoy, Fehmi
In this thesis, the Fisher’s equation is discretized in space with the symmetric interior point discontinuous Galerkin (SDIPG). As time integrator Kahan’s method is used, which is n efficient linearly implicit time integrator for PDE with quadratic nonlinearities like the Fisher’s equation. Numerical results for the SIPG method, Kahan’s method and mid-point method confirm the theoretically predicted convergence orders in space and time. Travelling waves with steep fronts are numerically well resolved in reaction dominated regimes.

Suggestions

Numerical simulation of advective Lotka-Volterra systems by discontinuous Galerkin method
Aktaş, Senem; Karasözen, Bülent; Uzunca, Murat; Department of Scientific Computing (2014)
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 ...
Exact solution of Schrodinger equation with deformed ring-shaped potential
Aktas, M; Sever, Ramazan (2005-01-01)
Exact solution of the Schrodinger equation with deformed ring-shaped potential is obtained in the parabolic and spherical coordinates. The Nikiforov-Uvarov method is used in the solution. Eigenfunctions and corresponding energy eigenvalues are calculated analytically. The agreement of our results is good.
Exact solutions of the radial Schrodinger equation for some physical potentials
IKHDAİR, SAMEER; Sever, Ramazan (2007-12-01)
By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained. (C) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.
Exact solution of Schrodinger equation for Pseudoharmonic potential
Sever, Ramazan; TEZCAN, CEVDET; Aktas, Metin; Yesiltas, Oezlem (2008-02-01)
Exact solution of Schrodinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The energy eigenvalues are calculated numerically for some values of l and n with n <= 5 for some diatomic molecules.
Discontinuous galerkin finite elements method with structure preserving time integrators for gradient flow equations
Sarıaydın Filibelioğlu, Ayşe; Karasözen, Bülent; Department of Scientific Computing (2015)
Gradient flows are energy driven evolutionary equations such that the energy decreases along solutions. There have been surprisingly a large number of well-known partial differential equations (PDEs) which have the structure of a gradient flow in different research areas such as fluid dynamics, image processing, biology and material sciences. In this study, we focus on two systems which can be modeled by gradient flows;Allen-Cahn and Cahn-Hilliard equations. These equations model the phase separation in mat...
Citation Formats
F. Özsoy, “Numerical solution of the Fisher’s equation with discontinous Galerkin method,” M.S. - Master of Science, Middle East Technical University, 2015.