Shifted fractional Legendre spectral collocation technique for solving fractional stochastic Volterra integro-differential equations

Doha E., Abdelkawy M., Amin A. Z. M. A., Lopes A. M.

Engineering with Computers, cilt.38, ss.1363-1373, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s00366-020-01263-w
  • Dergi Adı: Engineering with Computers
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1363-1373
  • Anahtar Kelimeler: Caputo fractional derivative, Fractional stochastic Volterra integro-differential equations, Gauss–Lobatto quadrature, Gauss–Radau quadrature, Spectral collocation method
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

This paper presents a spectral collocation technique to solve fractional stochastic Volterra integro-differential equations (FSV-IDEs). The algorithm is based on shifted fractional order Legendre orthogonal functions generated by Legendre polynomials. The shifted fractional order Legendre–Gauss–Radau collocation (SFL-GR-C) method is developed for approximating the FSV-IDEs, with the objective of obtaining a system of algebraic equations. For computational purposes, the Brownian motion function W(x) is discretized by Lagrange interpolation, while the integral terms are interpolated by Legendre–Gauss–Lobatto quadrature. Numerical examples demonstrate the accuracy and applicability of the proposed technique, even when dealing with non-smooth solutions.