Higher order numerical methods for solving fractional differential equations
In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 0. The order of convergence of the numerical method is O(h 3) for ??1 and O(h 1+2? ) for 0<??1 for sufficiently smooth solutions. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
fractional differential equation finite difference method caputo fractional derivative error estimates 26a33 65l70 65l05