Open AccessFast O(N) hybrid Laplace transform-finite difference method in solving 2D time fractional diffusion equation
Author(s) -
Fouad Mohammad Salama,
Norhashidah Hj. Mohd. Ali,
Nur Nadiah Abd Hamid
Publication year - 2020
Publication title -
journal of mathematics and computer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.218
H-Index - 5
ISSN - 2008-949X
DOI - 10.22436/jmcs.023.02.04
Subject(s) - laplace transform , finite difference method , mathematics , finite difference , convergence (economics) , finite difference coefficient , partial differential equation , laplace's equation , diffusion equation , fourier transform , stability (learning theory) , mathematical analysis , mathematical optimization , algorithm , computer science , finite element method , mixed finite element method , physics , economy , service (business) , machine learning , economics , thermodynamics , economic growth
It is time-memory consuming when numerically solving time fractional partial differential equations, as it requires O ( N 2 ) computational cost and O ( M N ) 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.