A High Order Numerical Algorithm for the Model of Viscoelastic Fractional Derivative

Abstract

In this paper, we construct a high order scheme to efficiently solve the forced vibration equation of viscoelastic material. The proposed method is based on a finite difference scheme in time. We used central difference scheme to the second derivative with second order accurate and 3ï€­ï¡ order accurate scheme to the fractional derivative of the orderï¡ ,0 ï€¼ï¡ ï€¼1. We obtain that the numerical scheme is second order. The convergence analysis is given that the numerical approximation of the exact solution accuracy as a second order. A series of numerical examples are given to verify the correctness of the theoretical analysis.