Date of Award

May 2018

Degree Type


Degree Name

Master of Science



First Advisor

Bruce A Wade

Committee Members

Istvan G Lauko, Lei Wang


Burgers' equation, Exponential time differencing, Finite differences, Numerical solutions, Pade, Real distinct poles


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.

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