Finding first order differential invariants through the $$S$$-function.(English)Zbl 1375.34056

Summary: The method presented in [the first and the second author, J. Math. Phys. 50, No. 1, 013514, 17 p. (2009; Zbl 1200.34039)] and [J. Avellar et al., Comput. Phys. Commun. 185, No. 1, 307–316 (2014; Zbl 1344.34002)] to search for first order invariants of second order ordinary differential equation (2ODEs) makes use of the so called Darboux polynomials. The main difficulty involved in this process is the determination of the Darboux polynomials, which is computationally very expensive. Here, we introduce an optional argument in the main routine that enables a shortcut in the calculations through the use of the $$S$$-function associated with the 2ODE.

MSC:

 34C14 Symmetries, invariants of ordinary differential equations 34-04 Software, source code, etc. for problems pertaining to ordinary differential equations 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms 68W30 Symbolic computation and algebraic computation

Citations:

Zbl 1200.34039; Zbl 1344.34002

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