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.

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  1. Choudhary, Renu; Singh, Satpal; Kumar, Devendra: A second-order numerical scheme for the time-fractional partial differential equations with a time delay (2022)
  2. Kumar, Surendra; Sharma, Abhishek; Pal Singh, Harendra: Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay (2021)
  3. Maleki, Mohammad; Davari, Ali: Analysis of an adaptive collocation solution for retarded and neutral delay systems (2021)
  4. Randall, E. Benjamin; Randolph, Nicholas Z.; Alexanderian, Alen; Olufsen, Mette S.: Global sensitivity analysis informed model reduction and selection applied to a Valsalva maneuver model (2021)
  5. Alzahrani, Ebraheem; Zeb, Anwar: Stability analysis and prevention strategies of tobacco smoking model (2020)
  6. Linh, Vu Hoang; Truong, Nguyen Duy: On convergence of continuous half-explicit Runge-Kutta methods for a class of delay differential-algebraic equations (2020)
  7. Randall, E. Benjamin; Randolph, Nicholas Z.; Olufsen, Mette S.: Persistent instability in a nonhomogeneous delay differential equation system of the Valsalva maneuver (2020)
  8. Zhao, Jingjun; Zhan, Rui; Xu, Yang: Explicit exponential Runge-Kutta methods for semilinear parabolic delay differential equations (2020)
  9. Xu, Xiuxiu; Huang, Qiumei: Superconvergence of discontinuous Galerkin methods for nonlinear delay differential equations with vanishing delay (2019)
  10. Sieber, Jan: Local bifurcations in differential equations with state-dependent delay (2017)
  11. Amat, Sergio; Legaz, M. José; Pedregal, Pablo: A variable step-size implementation of a variational method for stiff differential equations (2015)
  12. Guglielmi, Nicola; Hairer, Ernst: Numerical approaches for state-dependent neutral delay equations with discontinuities (2014)
  13. Khasi, M.; Ghoreishi, F.; Hadizadeh, M.: Numerical analysis of a high order method for state-dependent delay integral equations (2014)
  14. Lenz, Simon M.; Schlöder, Johannes P.; Bock, H. Georg: Numerical computation of derivatives in systems of delay differential equations (2014)
  15. Augustin, Florian; Gilg, Albert; Paffrath, Meinhard; Rentrop, Peter; Villegas, Manuel; Wever, Utz: An accuracy comparison of polynomial chaos type methods for the propagation of uncertainties (2013)
  16. Guglielmi, Nicola; Hairer, Ernst: Regularization of neutral delay differential equations with several delays (2013)
  17. Hartung, Ferenc: On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays (2013)
  18. Olufsen, Mette S.; Ottesen, Johnny T.: A practical approach to parameter estimation applied to model predicting heart rate regulation (2013)
  19. Khasawneh, Firas A.; Barton, David A. W.; Mann, Brian P.: Periodic solutions of nonlinear delay differential equations using spectral element method (2012)
  20. Rihan, Fathalla A.; Anwar, M. Naim: Qualitative analysis of delayed SIR epidemic model with a saturated incidence rate (2012)

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