On numerical solution of the time-fractional diffusion-wave equation with the fictitious time integration method

Hashemi M., Inc M., Parto-Haghighi M., BAYRAM M.

European Physical Journal Plus, vol.134, no.10, 2019 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 134 Issue: 10
  • Publication Date: 2019
  • Doi Number: 10.1140/epjp/i2019-12845-1
  • Journal Name: European Physical Journal Plus
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Istanbul Gelisim University Affiliated: Yes

Abstract

© 2019, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.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 ξ 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.