A new method of solving the differential equations by the formalization of mathematical operations of the computer
"Математика. Компьютер. Образование". Cб. трудов XIII международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2006. Vol. 2, 498pp. Pp. 295-307.
In the paper the solution of the differential equation is presented as a part of the series (of the powers of the step of the independent variable). Reducing the intermediate operations in the finite-difference scheme treated as a recurrent formula is used. On the basis of a general analogy with an operation of the computer the explicit form of the solution is constructed by means of the probabilistic methods. The approach is illustrated by solutions of several nonlinear equations.