Implementing Radau IIA methods for stiff delay differential equations.

*(English)*Zbl 0986.65069Summary: 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 |