论文信息 - Developing a delay differential equation solver - 字舞流文

Developing a delay differential equation solver

Abstract We discuss briefly various phenomena to be tested when designing a robust code for delay differential equations: choice of interpolant; tracking of discontinuities; vanishing delays; and problems arising from floating point arithmetic.

Christopher A. H. Paul | C. Paul

[1] Christopher T. H. Baker,et al. The tracking of derivative discontinuities in systems of delay-differential equations , 1992 .

[2] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[3] S. Filippi,et al. Stepsize control for delay differential equations using a pair of formulae , 1989 .

[4] J. Dormand,et al. A family of embedded Runge-Kutta formulae , 1980 .

[5] Herbert Arndt. Numerical solution of retarded initial value problems: Local and global error and stepsize control , 1984 .

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

[7] Jesper Oppelstrup,et al. The RKFHB4 method for delay — Differential equations , 1978 .

[8] Lucio Tavernini,et al. One-Step Methods for the Numerical Solution of Volterra Functional Differential Equations , 1971 .

[9] Desmond J. Higham,et al. Highly continuous Runge-Kutta interpolants , 1991, TOMS.

[10] M. Zennaro. Natural continuous extensions of Runge-Kutta methods , 1986 .

[11] S. Thompson,et al. Software for the numerical solution of systems of functional differential equations with state-dependent delays , 1992 .

[12] Alan Feldstein,et al. Characterization of jump discontinuities for state dependent delay differential equations , 1976 .