Browsing by Author "Cheyuo, Boniface Domonaamwin"

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    Numerical solution to fractional cattaneo heat equation in a semi-infinite medium
    (October 10, 2015) Cheyuo, Boniface Domonaamwin
    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.