A high order numerical method for solving Caputo nonlinear fractional ordinary differential equations

In this paper, we construct a high order numerical scheme for Caputo nonlinear fractional ordinary differential equations. Firstly, we use the piecewise Quadratic Lagrange interpolation method to construct a high order numerical scheme for Caputo nonlinear fractional ordinary differential equations, and then analyze the local truncation error of the high order numerical scheme. Secondly, based on the local truncation error, the convergence order of 3 - theta order is obtained. And the convergence are strictly analyzed. Finally, the numerical simulation of the high order numerical scheme is carried out. Through the calculation of typical problems, the effectiveness of the numerical algorithm and the correctness of theoretical analysis are verified.