Picture of aircraft jet engine

Strathclyde research that powers aerospace engineering...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by Strathclyde researchers involved in aerospace engineering and from the Advanced Space Concepts Laboratory - but also other internationally significant research from within the Department of Mechanical & Aerospace Engineering. Discover why Strathclyde is powering international aerospace research...

Strathprints also exposes world leading research from the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Equilibrium states of adaptive algorithms for delay differential equations

Higham, D.J. and Famelis, I.T. (1995) Equilibrium states of adaptive algorithms for delay differential equations. Journal of Computational and Applied Mathematics, 58 (2). pp. 151-169. ISSN 0377-0427

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

Abstract

This work examines the performance of explicit, adaptive, Runge-Kutta based algorithms for solving delay differential equations. The results of Hall (1985) for ordinary differential equation (ODE) solvers are extended by adding a constant-delay term to the test equation. It is shown that by regarding an algorithm as a discrete nonlinear map, fixed points or equilibrium states can be identified and their stability can be determined numerically. Specific results are derived for a low order Runge-Kutta pair coupled with either a linear or cubic interpolant. The qualitative performance is shown to depend upon the interpolation process, in addition to the ODE formula and the error control mechanism. Furthermore, and in contrast to the case for standard ODEs, it is found that the parameters in the test equation also influence the behaviour. This phenomenon has important implications for the design of robust algorithms. The choice of error tolerance, however, is shown not to affect the stability of the equilibrium states. Numerical tests are used to illustrate the analysis. Finally, a general result is given which guarantees the existence of equilibrium states for a large class of algorithms.