This article is cited in 8 papers

An efficient scheme for the implementation of implicit Runge–Kutta methods

L. M. Skvortsov

Bauman State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 107005, Russia

Abstract: A scheme is proposed for solving nonlinear algebraic equations arising in the implementation of the implicit Runge–Kutta methods. In contrast to the available schemes, not only the starting values of the variables but also those of the derivatives are predicted. This makes it possible to reduce the number of evaluations of the function (the right-hand side) at each implicit stage without significantly reducing the accuracy of integration.

Key words: implicit Runge–Kutta methods, modified Newton's iteration, starting values, stiffness.

UDC: 519.622

Received: 12.04.2008

 English version: Computational Mathematics and Mathematical Physics, 2008, 48:11, 2007–2017

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