Formation the term of order by Runge-Kutt methods using the method of labeled trees

Abstract

The theory of differential equation plays essential role in study of many processes and effects. Creation of effective algorithms of differential equations solving is important problem in theory of dynamic modeling and application programming. Using methods of high order for differential equation solving is a one way to increase precision and stability of solution. At this article a method of ‘rooted trees’ for creating differential equation solvers of high order is considered as a way aiming at rising computational precision of differential equations.