Journal of Applied Mathematics & Bioinformatics

The Implicit Keller Box method for the one dimensional time fractional diffusion equation

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  • Abstract

    There are a number of physical situations that can be modeled by fractional partial differential equations. In this paper, we discuss a numerical scheme based on Kellerís box method for one dimensional time fractional diffusion equation with boundary values which are functions. The fractional derivative term is replaced by the Grünwald-Letnikov formula. The stability is analyzed by means of the Von Neumann method. An example is presented to show the feasibility and the accuracy of this method and a comparison between the approximate solution using this method and analytical solution is made. The results indicated that this scheme is unconditionally stable and is a feasible technique.