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

Taylor series method, MATLAB, initial value problems, nonlinear ordinary differential equations

Most methods for solving ordinary differential equations use a limited order to calculate the results. The 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 nonlinear problems of ordinary differential equations and compare these approaches between one another and to the state-of-the-art solvers in MATLAB software.