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.


References in zbMATH (referenced in 23 articles )

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  1. Khasi, M.; Ghoreishi, F.; Hadizadeh, M.: Numerical analysis of a high order method for state-dependent delay integral equations (2014)
  2. Guglielmi, Nicola; Hairer, Ernst: Regularization of neutral delay differential equations with several delays (2013)
  3. Hartung, Ferenc: On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays (2013)
  4. Khasawneh, Firas A.; Barton, David A.W.; Mann, Brian P.: Periodic solutions of nonlinear delay differential equations using spectral element method (2012)
  5. Rihan, Fathalla A.; Anwar, M.Naim: Qualitative analysis of delayed SIR epidemic model with a saturated incidence rate (2012)
  6. Singh, Paramjeet; Sharma, Kapil K.: Numerical approximations to the transport equation arising in neuronal variability (2011)
  7. Barton, David A.W.; Krauskopf, Bernd; Wilson, R.Eddie: Nonlinear dynamics of torsional waves in a drill-string model with spatial extent (2010)
  8. Ali, Ishtiaq; Brunner, Hermann; Tang, Tao: Spectral methods for pantograph-type differential and integral equations with multiple delays (2009)
  9. Bellen, Alfredo; Guglielmi, Nicola: Solving neutral delay differential equations with state-dependent delays (2009)
  10. Huang, Chengming: Delay-dependent stability of high order Runge-Kutta methods (2009)
  11. Adhikari, Mohit H.; Coutsias, Evangelos A.; McIver, John K.: Periodic solutions of a singularly perturbed delay differential equation (2008)
  12. Guglielmi, Nicola; Hairer, Ernst: Computing breaking points in implicit delay differential equations (2008)
  13. Hartung, Ferenc: Linearized stability for a class of neutral functional differential equations with state-dependent delays (2008)
  14. Jain, Harsh V.; Nör, Jacques E.; Jackson, Trachette L.: Modeling the VEGF-Bcl-2-CXCL8 pathway in intratumoral agiogenesis (2008)
  15. Barton, David A.W.; Krauskopf, Bernd; Wilson, R.Eddie: Homoclinic bifurcations in a neutral delay model of a transmission line oscillator (2007)
  16. Aittokallio, T.; Gyllenberg, M.; Polo, O.; Toivonen, J.; Virkki, A.: Model-based analysis of mechanisms responsible for sleep-induced carbon dioxide differences (2006)
  17. Barton, David A.W.; Krauskopf, Bernd; Wilson, R.Eddie: Collocation schemes for periodic solutions of neutral delay differential equations (2006)
  18. Guglielmi, Nicola: Open issues in devising software for the numerical solution of implicit delay differential equations (2006)
  19. Hartung, Ferenc: Differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays (2006)
  20. Shampine, L.F.; Gahinet, P.: Delay-differential-algebraic equations in control theory (2006)

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