Barycentric interpolation collocation algorithm to solve fractional differential equations

Jin Li, Xiaoning Su and Kaiyan Zhao

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 205, issue C, 340-367

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.

Keywords: Barycentric interpolation; Collocation algorithm; Fractional differential equation; Gauss quadrature formula (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:205:y:2023:i:c:p:340-367

DOI: 10.1016/j.matcom.2022.10.005

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