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, cilt.134, sa.10, 2019 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 134 Sayı: 10
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1140/epjp/i2019-12845-1
  • Dergi Adı: European Physical Journal Plus
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

© 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.