Master Thesis

FZJ-2018-05282

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Numerical Solutions of Fractional Nonlinear Advection-Reaction-Diffusion Equations

Vorderwülbecke, S. (Corresponding author)FZJ*

2018

Abstract: In this thesis nonlinear differential equations containing advection, reaction and diffusionterms 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 spatialdiscretization. Furthermore, exponential time differencing schemes under consideration ofdifferent matrix exponential approximations are exploited for the temporal discretization,whereas finite differences are used for the spatial approximation. The schemes are applied tothe homogeneous Burgers, Burgers-Fisher and Burgers-Huxley equation and compared withrespect to convergence and efficiency in a numerical investigation.

Note: Masterarbeit, The University of Wisconsin-Milwaukee, 2018

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)

Appears in the scientific report 2018

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