Highly accurate technique for solving distributed-order time-fractional-sub-diffusion equations of fourth order

• DOI: 10.1007/s40314-020-1070-7
• Publication Date: 2020-02-11T15:02:46Z
• Authors: M. A. Abdelkawy; Mohammed M. Babatin; António M. Lopes
• Keywords: Algebraic equation; Quadrature (astronomy); Collocation (remote sensing)

This paper presents a new method for calculating the numerical solution of distributed-order time-fractional-sub-diffusion equations (DO-TFSDE) of fourth order. The method extends the shifted fractional Jacobi (SFJ) collocation scheme for discretizing both the time and space variables. The approximate solution is expressed as a finite expansion of SFJ polynomials whose derivatives are evaluated at the SFJ quadrature points. The process yields a system of algebraic equations that are solved analytically. The new method is compared with alternative numerical algorithms when solving different types of DO-TFSDE. The results show that the proposed method exhibits superior accuracy with an exponential convergence rate.