Jacobi Collocation Approximation for Solving Multi-dimensional Volterra Integral Equations

Abdelkawy M. A., Amin A. Z. M. A., Bhrawy A. H., Tenreiro MacHado J. A., Lopes A. M.

International Journal of Nonlinear Sciences and Numerical Simulation, cilt.18, sa.5, ss.411-425, 2017 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 5
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1515/ijnsns-2016-0160
  • Dergi Adı: International Journal of Nonlinear Sciences and Numerical Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.411-425
  • Anahtar Kelimeler: error analysis, shifted Jacobi polynomials, spectral collocation method, system of Volterra integral equation, Volterra integral equation
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

This paper addresses the solution of one- and two-dimensional Volterra integral equations (VIEs) by means of the spectral collocation method. The novel technique takes advantage of the properties of shifted Jacobi polynomials and is applied for solving multi-dimensional VIEs. Several numerical examples demonstrate the efficiency of the method and an error analysis verifies the correctness and feasibility of the proposed method when solving VIE.