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Implementing Radau IIA methods for stiff delay differential equations. (English) Zbl 0986.65069
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:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34K28Numerical approximation of solutions of functional-differential equations
65L80Numerical methods for differential-algebraic equations
34A09Implicit equations, differential-algebraic equations
34K40Neutral functional-differential equations
65L50Mesh generation and refinement (ODE)