Numerical solution to fractional cattaneo heat equation in a semi-infinite medium
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Date
October 10, 2015
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Abstract
In this study, a detailed review of the article published by Qi... et al. (2013) on
fractional Cattaneo heat equation in a semi-infnite medium has been made. In
reviewing this article, two fractional Cattaneo heat equations modeling the heat
flux and temperature distributions have been established and their exact solutions
proofed in detail forms. Firstly, the solution of the fractional Cattaneo heat flux equation is established using Laplace transform. secondly, the exact solution
of the fractional Cattaneo heat equation modeling temperature distribution is
established in a series form through Fox-function using Laplace transform (and
the inverse Laplace transform). In addition to the review, an implicit fnite
difference scheme has been used to solve the three c lasses of generalized fractional
Cattaneo heat equations (GCE's) in a semi-infnite medium. Three numerical
examples were provided using both the analytical solutions and finite difference
solutions to demonstrate the effects of fractional derivatives of orders
on temperature distributions. Graphical representation of the solutions were
presented using Matlab software. Finally, a comparison and discussion of the
analytical and finite difference scheme solutions from the graphs of the various
numerical examples have been made.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in
partial fulfillment of the requirement for the Degree of Master of Philosophy in Applied Mathematics, 2015