https://doi.org/10.1140/epjp/i2019-12845-1
Regular Article
On numerical solution of the time-fractional diffusion-wave equation with the fictitious time integration method
1
Department of Mathematics, Basic Science Faculty, University of Bonab, P.O. Box 55517-61167, Bonab, Iran
2
Department of Mathematics, Science Faculty, Firat University, Elazig, Turkey
3
Department of Computer Engineering, Gelisim University, Istanbul, Turkey
* e-mail: minc@firat.edu.tr
Received:
12
March
2019
Accepted:
22
June
2019
Published online:
4
October
2019
In this work we offer a robust numerical algorithm based on the Lie group to solve the time-fractional diffusion-wave (TFDW) equation. Firstly, we use a fictitious time variable to convert the related variable u(x, t) into a new space with one extra dimension. Then by using a composition of the group preserving scheme (GPS) and a semi-discretization of new variable, we approximate the solutions of the problem. Finally, various numerical experiments are performed to illustrate the power and accuracy of the given method.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019