A New S-Function Method searching for First Order Differential Integrals: Faster, Broader, Better

2023/06/11 by Duarte, L. G. S., da Mota, L. A. C. P., Nascimento, I. S. S.
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2306.06725

Abstract

Here we present a very efficient method to search for Liouvillian first integrals of second order rational ordinary differential equations (rational 2ODEs). This new algorithm can be seen as an improvement to the S-function method we have developed [24]. Here, we show how to further use the knowledge of the S-function to find an integrating factor of a set of first order rational ordinary differential equations (rational 1ODEs) which is shared by the original 2ODE, without having to actually solving these 1ODEs. This new use of the S-function, that is the theoretical basis of our new method to compute the integrating factor, proved to be a linear process of computation for a vast class of non-linear rational 2ODEs, making it much more efficient.

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