Abstract

The paper deals with a numerical solution of a special type of nonlinear-quadratic systems of Initial Value Problems of Ordinary Differential Equations. The research is focused on higher order and variable step size method based on Taylor series computation.

Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. The effective implementation of Modern Taylor Series Method in MATLAB software is introduced. The MTSM is based on automatic recurrent calculation of higher Taylor series terms. The computation time and accuracy of our approach are compared with MATLAB ode solvers on a set of nonlinear-quadratic ODE systems coming from real world technical problems.