TY - GEN

T1 - A variable step-size selection method for implicit integration schemes

AU - Holsapple, Raymond

AU - Iyer, Ram

AU - Doman, David

PY - 2006

Y1 - 2006

N2 - Implicit integration schemes, such as Runge-Kutta methods, are widely used in mathematics and engineering to numerically solve ordinary differential equations. Every integration method requires one to choose a step-size, h, for the integration. If h is too large or too small the efficiency of an implicit scheme is relatively low. As every implicit integration scheme has a global error inherent to the scheme, we choose the total number of computations in order to achieve a prescribed global error as a measure of efficiency of the integration scheme. In this paper, we propose the idea of choosing h by minimizing an efficiency function for general Runge-Kutta integration routines. We show the efficacy of this approach on some standard problems found in the literature.

AB - Implicit integration schemes, such as Runge-Kutta methods, are widely used in mathematics and engineering to numerically solve ordinary differential equations. Every integration method requires one to choose a step-size, h, for the integration. If h is too large or too small the efficiency of an implicit scheme is relatively low. As every implicit integration scheme has a global error inherent to the scheme, we choose the total number of computations in order to achieve a prescribed global error as a measure of efficiency of the integration scheme. In this paper, we propose the idea of choosing h by minimizing an efficiency function for general Runge-Kutta integration routines. We show the efficacy of this approach on some standard problems found in the literature.

UR - http://www.scopus.com/inward/record.url?scp=34047234654&partnerID=8YFLogxK

U2 - 10.1109/acc.2006.1657179

DO - 10.1109/acc.2006.1657179

M3 - Conference contribution

AN - SCOPUS:34047234654

SN - 1424402107

SN - 9781424402106

T3 - Proceedings of the American Control Conference

SP - 3013

EP - 3018

BT - Proceedings of the 2006 American Control Conference

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 14 June 2006 through 16 June 2006

ER -