Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis

Tedjani A., Amin A. Z. M. A., Abdel-Aty A., Abdelkawy M., Mahmoud M.

AIMS Mathematics, cilt.9, sa.4, ss.7973-8000, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3934/math.2024388
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.7973-8000
  • Anahtar Kelimeler: Caputo fractional derivative, convergence analysis, fractional Fredholm integro-differential equation, Legendre-Gauss-Lobatto, spectral method
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

The main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main idea is to use Caputo derivatives and Legendre-Gauss interpolation for nonlinear FFIDEs. A rigorous convergence analysis is provided and confirmed by numerical tests. In addition, we provide some numerical test cases to demonstrate that the approach can preserve the non-smooth solution of the underlying problem.