A Novel Numerical Method for Riemann-Liouville Fractional Differential Equation

Abstract

By using Hadamard finite-part integral formula and the quadratic interpolation method, a high order difference approximation scheme for the Riemann-Liouville fractional derivative is proposed. The scheme with truncation error order of O(h3-a ). For the fractional ordinary differential equation with Riemann-Liouville fractional derivative, a novel numerical method (D2 scheme) is derived. The numerical example shows that the proposed method is convergent, the numerical orders of convergence are consistent with 3 O(h3-a ) . Compared with other methods, the new method has the advantage of fast convergence speed and high precision.