A High-Order Scheme for Fractional Ordinary Differential Equations with the Caputo-Fabrizio Derivative

摘要

In this paper,we consider numerical solutions of fractional ordinary differential equations with the Caputo-Fabrizio derivative,and construct and analyze a high-order time-stepping scheme for this equation.The proposed method makes use of quadratic interpolation function in sub-intervals,which allows to produce fourth-order convergence.A rigorous stability and convergence analysis of the proposed scheme is given.A series of numerical examples are presented to validate the theoretical claims.Traditionally a scheme having fourth-order convergence could only be obtained by using block-by-block technique.The advantage of our scheme is that the solution can be obtained step by step,which is cheaper than a block-by-block-based approach.