Li, ZhiqiangYan, YubinFord, Neville J.2016-05-172016-05-172016-04-29Li, Z., Yan, Y., & Ford, N. J. (2016). Error estimates of a high order numerical method for solving linear fractional differential equations. Applied Numerical Mathematics, 114, 201-220. https://doi.org/10.1016/j.apnum.2016.04.01010.1016/j.apnum.2016.04.010http://hdl.handle.net/10034/609518In this paper, we first introduce an alternative proof of the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and the convergence order of the proposed numerical method is O(∆t 2−α ), 0 < α < 1, where α is the order of the fractional derivative and ∆t is the step size. We then use the similar idea to prove the error estimates of a high order numerical method for solving linear fractional differential equations proposed in Yan et al. [37], where a second-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and we show that the convergence order of the numerical method is O(∆t 3−α ), 0 < α < 1. The numerical examples are given to show that the numerical results are consistent with the theoretical results.enhttp://creativecommons.org/licenses/by-nc-nd/4.0/Fractional calculusNumerical methodsArticle1873-5460Applied Numerical Mathematics