Abstract: | We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividingthe domain into a number of subintervals, and applying the quadratic interpolationon each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order 3 − $ν$ can be rigorouslyproven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinearcase. Some numerical examples are given to validate our theoretical results. |