Approximate Solutions of Time Fractional Diffusion Wave Models

Abdul Ghafoor, Sirajul Haq, Manzoor Hussain, Poom Kumam and Muhammad Asif Jan
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Abdul Ghafoor: Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KP, Pakistan
Sirajul Haq: Faculty of Engineering Sciences, GIK Institute, Topi 23640, KP, Pakistan
Manzoor Hussain: Faculty of Engineering Sciences, GIK Institute, Topi 23640, KP, Pakistan
Poom Kumam: Theoretical and Computational Science (TaCS) Center Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
Muhammad Asif Jan: Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KP, Pakistan

Mathematics, 2019, vol. 7, issue 10, 1-15

Abstract: In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L 2 and L ∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before.

Keywords: fractional differential equations; two-dimensional wavelets; finite differences (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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