Fast \(O(N)\) hybrid Laplace transform-finite difference method in solving 2D time fractional diffusion equation

Volume 23, Issue 2, pp 110--123 http://dx.doi.org/10.22436/jmcs.023.02.04
Publication Date: October 15, 2020 Submission Date: May 12, 2020 Revision Date: August 15, 2020 Accteptance Date: September 15, 2020

Authors

Fouad Mohammad Salama - School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia. Norhashidah Hj. Mohd Ali - School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia. Nur Nadiah Abd Hamid - School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia.


Abstract

It is time-memory consuming when numerically solving time fractional partial differential equations, as it requires \(O(N^2)\) computational cost and \(O(MN)\) memory complexity with finite difference methods, where, \(N\) and \(M\) are the total number of time steps and spatial grid points, respectively. To surmount this issue, we develop an efficient hybrid method with \(O(N)\) computational cost and \(O(M)\) memory complexity in solving two-dimensional time fractional diffusion equation. The presented method is based on the Laplace transform method and a finite difference scheme. The stability and convergence of the proposed method are analyzed rigorously by the means of the Fourier method. A comparative study drawn from numerical experiments shows that the hybrid method is accurate and reduces the computational cost, memory requirement as well as the CPU time effectively compared to a standard finite difference scheme.


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ISRP Style

Fouad Mohammad Salama, Norhashidah Hj. Mohd Ali, Nur Nadiah Abd Hamid, Fast \(O(N)\) hybrid Laplace transform-finite difference method in solving 2D time fractional diffusion equation, Journal of Mathematics and Computer Science, 23 (2021), no. 2, 110--123

AMA Style

Salama Fouad Mohammad, Ali Norhashidah Hj. Mohd, Hamid Nur Nadiah Abd, Fast \(O(N)\) hybrid Laplace transform-finite difference method in solving 2D time fractional diffusion equation. J Math Comput SCI-JM. (2021); 23(2):110--123

Chicago/Turabian Style

Salama, Fouad Mohammad, Ali, Norhashidah Hj. Mohd, Hamid, Nur Nadiah Abd. "Fast \(O(N)\) hybrid Laplace transform-finite difference method in solving 2D time fractional diffusion equation." Journal of Mathematics and Computer Science, 23, no. 2 (2021): 110--123


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