Abstract Most methods for solving ordinary differential equations use a limited order to calculate the results. The higher-order method based on the Taylor series presented in this article can use as many terms of the Taylor series as necessary to obtain a stable and accurate solution. When solving nonlinear problems using this method, the solution can be complex. This paper introduces a new approach to solving nonlinear problems using the explicit Taylor series method. It compares this new approach against the previously used approach and the state-of-the-art solvers in MATLAB software.
Veigend et al. (Thu,) studied this question.