Numerical Solutions of Fractional Nonlinear Advection-Reaction-Diffusion Equations

Abstract

In this thesis nonlinear differential equations containing advection, reaction and diffusion terms are solved numerically, where the diffusion term is modelled by a fractional derivative. One of the methods employed is a finite difference method for temporal as well as spatial discretization. Furthermore, exponential time differencing schemes under consideration of different matrix exponential approximations are exploited for the temporal discretization, whereas finite differences are used for the spatial approximation. The schemes are applied to the homogeneous Burgers, Burgers-Fisher and Burgers-Huxley equation and compared with respect to convergence and efficiency in a numerical investigation.