Conference publications

Explicit Runge-Kutta schemes of 3-rd and 4-th order with exact estimation of truncation error

Butyaev V.A., Shirkov P.D.

"Математика. Компьютер. Образование". Cб. трудов XI международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2004. Vol. 2. Pp. 431-440.

For numerical solution of the Cauchy problem for ODE systems there are considered some modification of Runge-Kutta schemes, which are based on using of Jacoby matrix as well as for calculation of stadies as for estimation of the truncation error. There were found some methods of the 4-th order of accuracy. They have been carrefully studied numerically and show their rubastness and efficiency being compering with wellknown methods of the 4-th and 5-th order, which are ussially used in apllied codes.

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