Taylor series based numerical integration method for solution of nonlinear problems with division

Most methods for solving ordinary differential equations use a limited order to calculate the results. The higher order method presented in this article can use as many terms of the Taylor series as necessary to obtain a stable and accurate solution. The solution using this method (particularly for nonlinear problems) can be quite complex. The aim of this article is to compare several ways of expressing the operation division in the nonlinear problems of ordinary differential equations and compare these approaches with one another and to the state-of-the-art solvers in MATLAB software.