Implementing Radau IIA methods for
stiff delay differential equations
Nicola Guglielmi and Ernst Hairer
Abstract.
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 encountered
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 at several examples,
and it is compared to existing programs.
Key Words.
Stiff delay differential equations, vanishing delay,
implicit Runge-Kutta methods, implementation.