ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 65 Kulikov, Gennady Yur’evich, Ulyanovsk State University, Russia How to control the global error of Runge-Kutta methods In this paper we develop a new procedure to control stepsize for Runge-Kutta methods. In contrast to the standard approach, the error control mechanism presented here is based on monitoring and controlling both the local and global errors of Runge-Kutta formulas. As a result, Runge-Kutta methods with the local-global stepsize control solve differential or differential-algebraic equations with any prescribed accuracy (up to roundoff errors). For implicit Runge-Kutta formulas we give the sufficient number of both full and modified Newton iterations allowing the iterative approximations to be correctly used in the local-global stepsize control. In addition, we develop a stable local-global error control mechanism which is applicable for stiff problems.