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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:
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
Software:
RADAR5
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