Journal of Applied Mathematics

Symbolic Solution to Complete Ordinary Differential Equations with Constant Coefficients

Juan F. Navarro and Antonio Pérez-Carrió

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Abstract

The aim of this paper is to introduce a symbolic technique for the computation of the solution to a complete ordinary differential equation with constant coefficients. The symbolic solution is computed via the variation of parameters method and, thus, constructed over the exponential matrix of the linear system associated with the homogeneous equation. This matrix is also symbolically determined. The accuracy of the symbolic solution is tested by comparing it with the exact solution of a test problem.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 518194, 15 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808104

Digital Object Identifier
doi:10.1155/2013/518194

Mathematical Reviews number (MathSciNet)
MR3094957

Zentralblatt MATH identifier
06950720

Citation

Navarro, Juan F.; Pérez-Carrió, Antonio. Symbolic Solution to Complete Ordinary Differential Equations with Constant Coefficients. J. Appl. Math. 2013 (2013), Article ID 518194, 15 pages. doi:10.1155/2013/518194. https://projecteuclid.org/euclid.jam/1394808104


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References

  • H. Poincare, Les Methodes Nouvelles de la Mecanique Celeste I, Gauthiers-Villars, Paris, France, 1892.
  • J. Henrard, “A survey of Poisson series processors,” Celestial Mechanics, vol. 45, no. 1–3, pp. 245–253, 1989.
  • A. Deprit, J. Henrard, and A. Rom, “La theorie de la lune de Delaunay et son prolongement,” Comptes Rendus de l'Académie des Sciences, vol. 271, pp. 519–520, 1970.
  • A. Deprit, J. Henrard, and A. Rom, “Analytical Lunar Ephemeris: Delaunay's theory,” The Astronomical Journal, vol. 76, pp. 269–272, 1971.
  • J. Henrard, “A new solution to the Main Problem of Lunar Theory,” Celestial Mechanics, vol. 19, no. 4, pp. 337–355, 1979.
  • M. Chapront-Touze, “La solution ELP du probleme central de la Lune,” Astronomy & Astrophysics, vol. 83, pp. 86–94, 1980.
  • M. Chapront-Touze, “Progress in the analytical theories for the orbital motion of the Moon,” Celestial Mechanics, vol. 26, no. 1, pp. 53–62, 1982.
  • J. F. Navarro and J. M. Ferrándiz, “A new symbolic processor for the Earth rotation theory,” Celestial Mechanics & Dynamical Astronomy, vol. 82, no. 3, pp. 243–263, 2002.
  • J. F. Navarro, “On the implementation of the Poincaré-Lindstedt technique,” Applied Mathematics and Computation, vol. 195, no. 1, pp. 183–189, 2008.
  • J. F. Navarro, “Computation of periodic solutions in perturbed second-order ODEs,” Applied Mathematics and Computation, vol. 202, no. 1, pp. 171–177, 2008.
  • J. F. Navarro, “On the symbolic computation of the solution to a differential equation,” Advances and Applications in Mathematical Sciences, vol. 1, no. 1, pp. 1–21, 2009.
  • J. F. Navarro and A. Pérez, “Principal matrix of a linear system symbolically computed,” in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM '08), pp. 400–402, September 2008.
  • C. Moler and C. van Loan, “Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later,” SIAM Review, vol. 45, no. 1, pp. 3–49, 2003.
  • J. F. Navarro and A. Pérez, “Symbolic computation of the solution to an homogeneous ODE with constant coefficients,” in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM '09), pp. 400–402, 2009.