Picture of wind turbine against blue sky

Open Access research with a real impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

The Energy Systems Research Unit (ESRU) within Strathclyde's Department of Mechanical and Aerospace Engineering is producing Open Access research that can help society deploy and optimise renewable energy systems, such as wind turbine technology.

Explore wind turbine research in Strathprints

Explore all of Strathclyde's Open Access research content

Global error versus tolerance for explicit Runge-Kutta methods

Higham, Desmond J. (1991) Global error versus tolerance for explicit Runge-Kutta methods. IMA Journal of Numerical Analysis, 11 (4). pp. 457-480. ISSN 0272-4979

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

Initial value solvers typically input a problem specification and an error tolerance, and output an approximate solution. Faced with this situation many users assume, or hope for, a linear relationship between the global error and the tolerance. In this paper we examine the potential for such 'tolerance proportionality' in existing explicit Runge-Kutta algorithms. We take account of recent developments in the derivation of high-order formulae, defect control strategies, and interpolants for continuous solution and first derivative approximations. Numerical examples are used to verify the theoretical predictions. The analysis draws on the work of Stetter, and the numerical testing makes use of the nonstiff DETEST package of Enright and Pryce.