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Barycentric interpolation collocation algorithm to solve fractional differential equations

Author

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  • Li, Jin
  • Su, Xiaoning
  • Zhao, Kaiyan

Abstract

Fractional equations have been paid much attention in recent years. Barycentric interpolation collocation algorithm (BICA) is proposed to solve the fractional differential equations in this manuscript. In order to calculate fractional derivatives in fractional differential equations, the Gauss quadrature formula with weights ρ(τ)=(t−τ)ξ−α is constructed and the error estimation of this quadrature formula is proved. The fractional differential term of equation is transformed into Riemann integral under Caputo definition. Barycentric interpolation is used to approximate the unknown function and matrix equation of transformed fractional differential equation is obtained by BICA. The error results show exponential convergence rate of Gauss quadrature formula with weights ρ(τ)=(t−τ)ξ−α by comparing with the Gauss–Legendre quadrature formula. In addition, several examples are given to solve the fractional differential equation.

Suggested Citation

  • Li, Jin & Su, Xiaoning & Zhao, Kaiyan, 2023. "Barycentric interpolation collocation algorithm to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 340-367.
  • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:340-367
    DOI: 10.1016/j.matcom.2022.10.005
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    References listed on IDEAS

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