| Abstract: | 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. |
