Two FORTRAN packages for assessing initial value methods. We present a discussion and description of a collection of FORTRAN routines designed to aid in the assessment of initial value methods for ordinary differential equations. Although the overall design characteristics are similar to those of earlier testing packages that were used for the comparison of methods, the details and objectives of the current collection are quite different. Our principal objective is the development of testing tools that can be used to assess the efficiency and reliability of a standard numerical method without requiring significant modifications to the method and without the tools themselves affecting the performance of the method. [For the algorithm NSDTST and STDTST: Routine for assessing the performance of IV solvers. see ibid. 13, 28-34 (1987)].

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 79 articles , 1 standard article )

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  1. Simos, T. E.; Tsitouras, Ch.: On high order Runge-Kutta-Nyström pairs (2022)
  2. Ernsthausen, John M.; Nedialkov, Nedialko S.: Stepsize selection in the rigorous defect control of Taylor series methods (2020)
  3. Marciniak, Andrzej; Jankowska, Malgorzata A.: Interval methods of Adams-Bashforth type with variable step sizes (2020)
  4. Marciniak, Andrzej; Jankowska, Malgorzata A.: Interval versions for special kinds of explicit linear multistep methods (2020)
  5. Mirkarim, Malihe Baigom; Basiri, Abdolali; Rahmany, Sajjad: Solving stiff systems by using symbolic-numerical method (2020)
  6. Kennedy, Christopher A.; Carpenter, Mark H.: Higher-order additive Runge-Kutta schemes for ordinary differential equations (2019)
  7. Marciniak, Andrzej; Jankowska, Malgorzata A.: Interval versions of Milne’s multistep methods (2018)
  8. Pryce, John D.; Nedialkov, Nedialko S.; Tan, Guangning; Li, Xiao: How AD can help solve differential-algebraic equations (2018)
  9. Marciniak, Andrzej; Jankowska, Malgorzata A.; Hoffmann, Tomasz: On interval predictor-corrector methods (2017)
  10. Nguyen-Ba, Truong: On variable step Hermite-Birkhoff solvers combining multistep and 4-stage DIRK methods for stiff ODEs (2016)
  11. Nguyen-Ba, Truong; Giordano, Thierry: On variable step highly stable 4-stage Hermite-Birkhoff solvers for stiff ODEs (2016)
  12. Kroshko, Andrew; Spiteri, Raymond J.: odeToJava: a PSE for the numerical solution of IVPS (2015)
  13. Nguyen-Ba, Truong; Giordano, Thierry; Vaillancourt, Rémi: Three-stage Hermite-Birkhoff solver of order 8 and 9 with variable step size for stiff ODEs (2015)
  14. Abhulimen, C. E.: Exponentially fitted third derivative three-step methods for numerical integration of stiff initial value problems (2014)
  15. Nguyen-Ba, Truong; Desjardins, Steven J.; Sharp, Philip W.; Vaillancourt, Rémi: Contractivity-preserving explicit Hermite-Obrechkoff ODE solver of order 13 (2013)
  16. Sharp, Philip W.; Qureshi, Mohammad A.; Grazier, Kevin R.: High order explicit Runge-Kutta Nyström pairs (2013)
  17. Auer, Ekaterina; Rauh, Andreas: VERICOMP: A system to compare and assess verified IVP solvers (2012)
  18. Canedo, Arquimedes; Yoshizawa, Takeo; Komatsu, Hideaki; Kobayashi, Mei: RK-slim: embedded Runge-Kutta without the excess baggage (2011)
  19. Tsitouras, Ch.: Runge-Kutta pairs of order (5(4)) satisfying only the first column simplifying assumption (2011)
  20. Enright, W. H.; Yan, Li: The reliability/cost trade-off for a class of ODE solvers (2010)

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