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 69 articles )

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  1. Marciniak, Andrzej; Jankowska, Malgorzata A.; Hoffmann, Tomasz: On interval predictor-corrector methods (2017)
  2. Nguyen-Ba, Truong: On variable step Hermite-Birkhoff solvers combining multistep and 4-stage DIRK methods for stiff ODEs (2016)
  3. Nguyen-Ba, Truong; Giordano, Thierry: On variable step highly stable 4-stage Hermite-Birkhoff solvers for stiff ODEs (2016)
  4. Kroshko, Andrew; Spiteri, Raymond J.: odeToJava: a PSE for the numerical solution of IVPS (2015)
  5. 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)
  6. Sharp, Philip W.; Qureshi, Mohammad A.; Grazier, Kevin R.: High order explicit Runge-Kutta Nyström pairs (2013)
  7. Auer, Ekaterina; Rauh, Andreas: VERICOMP: A system to compare and assess verified IVP solvers (2012)
  8. Canedo, Arquimedes; Yoshizawa, Takeo; Komatsu, Hideaki; Kobayashi, Mei: RK-slim: embedded Runge-Kutta without the excess baggage (2011)
  9. Tsitouras, Ch.: Runge-Kutta pairs of order $5(4)$ satisfying only the first column simplifying assumption (2011)
  10. Enright, W.H.; Yan, Li: The reliability/cost trade-off for a class of ODE solvers (2010)
  11. Nguyen-Ba, Truong; Bozic, Vladan; Kengne, Emmanuel; Vaillancourt, Rémi: A one-step 7-stage Hermite-Birkhoff-Taylor ODE solver of order 11 (2010)
  12. Verner, J.H.: Numerically optimal Runge-Kutta pairs with interpolants (2010)
  13. Nguyen-Ba, Truong; Hao, Han; Yagoub, Hemza; Vaillancourt, Rémi: One-step 5-stage Hermite-Birkhoff-Taylor ODE solver of order 12 (2009)
  14. Psihoyios, G.: A family of numerical multistep methods with three distinct schemes: explicit advanced step-point (EAS) methods and the EAS1 approach (2009)
  15. Psihoyios, G.: Explicit advanced step-point (EAS) methods and the EAS2 multistep scheme for the solution of non-stiff initial value problems (2009)
  16. Tsitouras, Ch.: Runge-Kutta interpolants for high precision computations (2007)
  17. Barrio, R.; Blesa, F.; Lara, M.: VSVO formulation of the Taylor method for the numerical solution of ODEs (2005)
  18. González-Pinto, S.; Rojas-Bello, R.: Speeding up Newton-type iterations for stiff problems (2005)
  19. Psihoyios, G.: A class of implicit advanced step-point methods with a parallel feature for the solution of stiff initial value problems (2004)
  20. González-Pinto, S.; Montijano, J.I.; Pérez-Rodríguez, S.: Variable-order starting algorithms for implicit Runge-Kutta methods on stiff problems (2003)

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