THERMAL SCIENCE

International Scientific Journal

Mir Sajjad Hashemi

,

Dumitru Baleanu

,

Mohammad Parto-Haghighi

,

Elham Darvishi

SOLVING THE TIME-FRACTIONAL DIFFUSION EQUATION USING A LIE GROUP INTEGRATOR

ABSTRACT
In this paper, we propose a numerical method to approximate the solutions of time fractional diffusion equation which is in the class of Lie group integrators. Our utilized method, namely fictitious time integration method transforms the unknown dependent variable to a new variable with one dimension more. Then the group preserving scheme is used to integrate the new fractional partial differential equations in the augmented space R3+1. Effectiveness and validity of method demonstrated using two examples.
KEYWORDS
time fractional diffusion equation, fictitious time integration method, caputo fractional derivative, group-preserving scheme
PAPER SUBMITTED: 2014-11-15
PAPER REVISED: 2015-02-02
PAPER ACCEPTED: 2015-03-04
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S77H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S77 - S83]
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Solving the time-fractional diffusion equation using a lie group integrator

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence