Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

AHMED ZAKI MAHAMED AMIN A. Z. M. A., Abdelkawy M., Amin A. K., Lopes A. M., Alluhaybi A. A., Hashim I.

AIMS Mathematics, cilt.8, sa.9, ss.20871-20891, 2023 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 9
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3934/math.20231063
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.20871-20891
  • Anahtar Kelimeler: shifted Legendre polynomials, shifted Legendre-Gauss-Lobatto quadrature, spectral collocation method, system of mixed Volterra-Fredholm integral equations
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.