Integrating factors for second order ODEs

Details Integrating factors for second order ODEs Integrating factors for second order ODEs

2000-02-08

arxiv.org/abs/math-ph/0002025v1

Journal of Symbolic Computation, V. 27, No. 5, pp. 501-519 (1999)

Physics

Mathematical Physics

21 pages - original version submitted Nov/1997. Related Maple programs for finding integrating factors together with the ODEto

Scientific paper

A systematic algorithm for building integrating factors of the form mu(x,y), mu(x,y') or mu(y,y') for second order ODEs is presented. The algorithm can determine the existence and explicit form of the integrating factors themselves without solving any differential equations, except for a linear ODE in one subcase of the mu(x,y) problem. Examples of ODEs not having point symmetries are shown to be solvable using this algorithm. The scheme was implemented in Maple, in the framework of the "ODEtools" package and its ODE-solver. A comparison between this implementation and other computer algebra ODE-solvers in tackling non-linear examples from Kamke's book is shown.

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