论文信息 - Stepsize control and continuity consistency for state-dependent delay-differential equations

Stepsize control and continuity consistency for state-dependent delay-differential equations

Abstract Derivative discontinuities occur frequently in the solutions of delay-differential equations, even when the functions defining them are all C ∞ . Unless correctly treated, such discontinuities can undermine the continuity assumptions made by ODE software. In this paper we discuss some specific difficulties arising from this aspect in the treatment of state-dependent problems. A necessary property, continuity consistency , is introduced along with a class of methods for which it is satisfied.

Christopher T. H. Baker | David R. Willé

[1] P. Hartman. Ordinary Differential Equations , 1965 .

[2] M. R. Osborne,et al. The numerical solution of differential equations , 1961 .

[3] Alan Feldstein,et al. High Order Methods for State-Dependent Delay Differential Equations with Nonsmooth Solutions , 1984 .

[4] Kenneth W. Neves. Automatic Integration of Functional Differential Equations: An Approach , 1975, TOMS.

[5] Christopher T. H. Baker,et al. DELSOL: a numerical code for the solution of systems of delay-differential equations , 1992 .

[6] Christopher T. H. Baker,et al. Parallel continuous Runge-Kutta methods and vanishing lag delay differential equations , 1993, Adv. Comput. Math..

[7] John C. Butcher. The adaptation of STRIDE to delay differential equations , 1992 .

[8] J. Butcher. The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[9] L. Collatz. The numerical treatment of differential equations , 1961 .

[10] H. J. Pesch,et al. Numerical treatment of delay differential equations by Hermite Interpolation , 1981 .