AN EXPLICIT ESTIMATE FOR APPROXIMATE SOLUTIONS OF ODES BASED ON THE TAYLOR FORMULA

Abstract

In this paper, we consider a third-order explicit scheme based on Taylor's formula to obtain an approximate solution for the Cauchy problem of systems of ODEs. We prove an estimate for the accuracy of the approximate solution with an explicit constant that depends only on the right-hand side of the equation and the domain of the solution.

Keywords

• dynamical systems, cauchy problem, approximate solution, taylor formula, accuracy precision of an approximate solution, level of accuracy, error term