DIMSIM

Experiments with a variable-order type 1 DIMSIM code. A new code for nonstiff ordinary differential equations is discussed. It is based on the Nordsieck representation of type 1 diagonally implicit multistage integration methods (DIMSIMs), implemented in a variable-step size variable-order mode. The code outperforms the Matlab {it ode45} code for moderate and stringent tolerances.

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References in zbMATH (referenced in 21 articles , 1 standard article )

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  1. Almasoodi, A. Y. J.; Abdi, A.; Hojjati, G.: A GLMs-based difference-quadrature scheme for Volterra integro-differential equations (2021)
  2. Abdi, Ali; Conte, Dajana: Implementation of second derivative general linear methods (2020)
  3. Abdi, Ali; Hojjati, Gholamreza: Projection of second derivative methods for ordinary differential equations with invariants (2020)
  4. Abdi, Ali; Hojjati, Gholamreza; Sharifi, Mohammad: Implicit-explicit second derivative diagonally implicit multistage integration methods (2020)
  5. Abdi, A.; Jackiewicz, Z.: Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability (2019)
  6. Califano, G.; Izzo, G.; Jackiewicz, Z.: Starting procedures for general linear methods (2017)
  7. Famelis, I. Th.; Jackiewicz, Z.: A new approach to the construction of DIMSIMs of high order and stage order (2017)
  8. Cardone, Angelamaria; Jackiewicz, Zdzisław; Verner, James H.; Welfert, Bruno: Order conditions for general linear methods (2015)
  9. Braś, M.: Nordsieck methods with inherent quadratic stability (2011)
  10. Izzo, G.; Jackiewicz, Z.; Messina, E.; Vecchio, A.: General linear methods for Volterra integral equations (2010)
  11. Jackiewicz, Zdzisław: General linear methods for ordinary differential equations (2009)
  12. Jackiewicz, Z.; Zubik-Kowal, B.: Discrete variable methods for delay-differential equations with threshold-type delays (2009)
  13. Kulikov, G. Yu.; Shindin, S. K.: Local and global error estimation in Nordsieck methods (2008)
  14. Butcher, J. C.; Jackiewicz, Z.; Wright, W. M.: Error propagation of general linear methods for ordinary differential equations (2007)
  15. Hoppensteadt, F. C.; Jackiewicz, Z.: Numerical solution of a problem in the theory of epidemics (2006)
  16. Jackiewicz, Z.: Construction and implementation of general linear methods for ordinary differential equations: a review (2005)
  17. Butcher, J. C.; Jackiewicz, Z.: A new approach to error estimation for general linear methods (2003)
  18. Jackiewicz, Z.: Implementation of DIMSIMs for stiff differential systems (2002)
  19. Butcher, J. C.; Jackiewicz, Z.: A reliable error estimation for diagonally implicit multistage integration methods (2001)
  20. Wright, W. M.: The construction of order 4 DIMSIMs for ordinary differential equations (2001)

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