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LIE TRANSFORMS FOR ORDINARY DIFFERENTIAL EQUATIONS: TAKING ADVANTAGE OF THE HAMILTONIAN FORM OF TERMS OF THE PERTURBATION
Author(s) -
BARRIO ROBERTO,
PALACIÁN JESÚS
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970630)40:12<2289::aid-nme165>3.0.co;2-j
Subject(s) - mathematics , hamiltonian (control theory) , ordinary differential equation , algebra over a field , perturbation (astronomy) , hamiltonian system , lie group , mathematical analysis , differential equation , pure mathematics , mathematical optimization , physics , quantum mechanics
In the context of Lie transforms theory applied to ordinary differential systems, we deal with the case for which part of the perturbing equation admits a Hamiltonian formulation. This fact allows to perform a Lie transform combining a treatment of vector type with another of Hamiltonian character. We show that this produces a reduction in the number of operations involved in the algorithms. We illustrate the algorithms with an example. © 1997 John Wiley & Sons, Ltd.