RADAR5
Implementing Radau IIA methods for stiff delay differential equations. 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.
Keywords for this software
References in zbMATH (referenced in 30 articles )
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- Guglielmi, Nicola; Hairer, Ernst: Regularization of neutral delay differential equations with several delays (2013)
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- Khasawneh, Firas A.; Barton, David A. W.; Mann, Brian P.: Periodic solutions of nonlinear delay differential equations using spectral element method (2012)
- Rihan, Fathalla A.; Anwar, M. Naim: Qualitative analysis of delayed SIR epidemic model with a saturated incidence rate (2012)
- Boer, H. M. T.; Stötzel, C.; Röblitz, S.; Deuflhard, P.; Veerkamp, R. F.; Woelders, H.: A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions (2011)
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- Rihan, Fathalla A.: Computational methods for delay parabolic and time-fractional partial differential equations (2010)
- Ali, Ishtiaq; Brunner, Hermann; Tang, Tao: Spectral methods for pantograph-type differential and integral equations with multiple delays (2009)
- Bellen, Alfredo; Guglielmi, Nicola: Solving neutral delay differential equations with state-dependent delays (2009)
- Huang, Chengming: Delay-dependent stability of high order Runge-Kutta methods (2009)
- Adhikari, Mohit H.; Coutsias, Evangelos A.; McIver, John K.: Periodic solutions of a singularly perturbed delay differential equation (2008)
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- Hartung, Ferenc: Linearized stability for a class of neutral functional differential equations with state-dependent delays (2008)
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