Implementing Radau IIA methods for stiff delay differential equations. (English) Zbl 0986.65069

Guglielmi, N.; Hairer, E.

Computing 67, No. 1, 1-12 (2001).

Summary: This article discusses the numerical solution of a general class of delay differential equations, including stiff problems, differential-algebraic delay equations, and neutral problems. The delays can be state dependent, and they are allowed to become small and vanish during the integration. Difficulties encounted in the implementation of implicit Runge-Kutta methods are explained, and it is shown how they can be overcome. The performance of the resulting code – RADAR5 – is illustrated on several examples, and it is compared to existing programs.

MSC:

65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05	Numerical methods for initial value problems
34K28	Numerical approximation of solutions of functional-differential equations (MSC2010)
65L80	Numerical methods for differential-algebraic equations
34A09	Implicit ordinary differential equations, differential-algebraic equations
34K40	Neutral functional-differential equations
65L50	Mesh generation, refinement, and adaptive methods for ordinary differential equations

Keywords:

numerical examples; stiff delay differential equation; neutral problems; Runge-Kutta methods; step size control; numerical comparisons; differential-algebraic delay equations; performance

Software:

RADAR5