ODEtools

Computer algebra solving of first order ODEs using symmetry methods. A Maple V R.3/4 computer algebra package, ODEtools, for the analytical solving of first-order ordinary differential equations (ODEs) using Lie group symmetry methods is presented. The set of commands includes a first-order ODE solver and routines for, among other things: the explicit determination of the coefficients of the infinitesimal symmetry generator; the construction of the most general invariant first-order ODE under given symmetries; the determination of the canonical coordinates of the underlying invariant group; and the testing of the returned results.


References in zbMATH (referenced in 11 articles )

Showing results 1 to 11 of 11.
Sorted by year (citations)

  1. Malykh, M. D.: On transcendental functions arising from integrating differential equations in finite terms (2015)
  2. Michoski, C. E.; Evans, J. A.; Schmitz, P. G.: Discontinuous Galerkin (h p)-adaptive methods for multiscale chemical reactors: quiescent reactors (2014)
  3. Dridi, Raouf; Petitot, Michel: New classification techniques for ordinary differential equations (2009)
  4. Gehrs, Kai: Integrating factors of some classes of third-order ODEs (2008)
  5. Avellar, J.; Duarte, L. G. S.; Duarte, S. E. S.; da Mota, L. A. C. P.: A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations (2007)
  6. Avellar, J.; Duarte, L. G. S.; Duarte, S. E. S.; Da Mota, L. A. C. P.: Determining Liouvillian first integrals for dynamical systems in the plane (2007)
  7. Bradshaw-Hajek, B. H.; Edwards, M. P.; Broadbridge, P.; Williams, G. H.: Nonclassical symmetry solutions for reaction-diffusion equations with explicit spatial dependence (2007)
  8. Gehrs, Kai Frederik: Algorithmic methods for ordinary differential equations (2006)
  9. Duarte, L. G. S.; Duarte, S. E. S.; Da Mota, L. A. C. P.; Skea, J. E. F.: An extension of the Prelle-Singer method and a Maple implementation (2002)
  10. Cheb-Terrab, E. S.; Duarte, L. G. S.; da Mota, L. A. C. P.: Computer algebra solving second order ODEs using symmetry methods (1998)
  11. Cheb-Terrab, E. S.; Duarte, L. G. S.; Da Mota, L. A. C. P.: Computer algebra solving of first order ODEs using symmetry methods (1997)