Solving a Class of Time-Fractional Order Par-tial Differential Equations in High Order Scheme

Abstract

This paper investigates the numerical solution of a class of partial differential equations of time-fractional order. Firstly, the paper discretizes the spatial variables using the higher order weighted essential no oscillation (WENO) scheme to achieve high accuracy in the spatial direction, thus obtaining an ordinary differential equation related only to time. Then, the exponential sum approximation (SOE) to the time-fractional order Caputo derivative is applied in the time direction to reduce memory and complexity for fast computation. Next, the higher-order convergence of the