Solutions of Time-Fractional Diffusion Equation with Reflecting and Absorbing Boundary Conditions Using Matlab

Iftikhar Ali (), Nadeem A. Malik and Bilal Chanane
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Iftikhar Ali: King Fahd University of Petroleum and Minerals
Nadeem A. Malik: King Fahd University of Petroleum and Minerals
Bilal Chanane: King Fahd University of Petroleum and Minerals

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 15-25 from Springer

Abstract: Abstract The main objective of this work is to develop Matlab programs for solving the time-fractional diffusion equation (TFDE) with reflecting and absorbing boundary conditions on finite and infinite domains. Essentially, there are three major codes, one for finding the exact solution of the TFDE and other two are for finding the numerical solution of the TFDE. The code for finding the exact solutions is based on the fundamental solution of the TFDE, whereas the codes for finding the numerical solutions are based on the explicit and the implicit finite difference schemes, respectively. Finally, we illustrate the effectiveness of the codes by applying them to TFDEs with sharp initial data and for various reflecting and absorbing boundary conditions both on finite and infinite domains. The results show the difference of solutions between the standard diffusion equation and the time-fractional diffusion equation.

Keywords: Time-fractional Diffusion Equation (TFDE); Absorbing Boundary Conditions; Explicit Finite Difference Scheme; Developed MATLAB Program; CTRW Framework (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_2

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DOI: 10.1007/978-3-319-30379-6_2

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