A local-global version of a stepsize control for Runge-Kutta methods

Research paper by G. Y. Kulikov

Indexed on: 01 May '00Published on: 01 May '00Published in: Journal of Applied Mathematics and Computing


In this paper we develop a new procedure to control stepsize for Runge-Kutta methods applied to both ordinary differential equations and semi-explicit index 1 differential-algebraic equations. 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 round-off 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 procedure of the local-global stepsize control. In addition, we develop a stable local-global error control mechanism which is applicable for stiff problems. Numerical tests support the theoretical results of the paper.