A tau method based on Jacobi operational matrix for solving fractional telegraph equation with Riesz-space derivative

Bonyadi S., Mahmoudi Y., Lakestanı M., Jahangiri Rad M.

Computational and Applied Mathematics, cilt.39, sa.4, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s40314-020-01363-9
  • Dergi Adı: Computational and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Anahtar Kelimeler: Error bound, Fractional telegraph equation, Operational matrix, Riesz fractional derivative, Shifted Jacobi tau method
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, we have presented an accurate and impressive spectral algorithm for solving fractional telegraph equation with Riesz-space derivative and Dirichlet boundary conditions. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrices of Riemann–Liouville fractional integral and left- and right-sided Caputo fractional derivatives. Primarily, we implement the proposed algorithm in both temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations which considerably simplifies the problem. In addition, an error bound is established in the L∞-norm for the suggested spectral Jacobi tau method. Illustrative examples are included to demonstrate the validity and accuracy of the presented technique.