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arXiv · 2306.06725

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

L. G. S. Duarte·L. A. C. P. da Mota·I. S. S. Nascimento
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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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L. G. S. Duarte, L. A. C. P. da Mota, I. S. S. Nascimento. 2023-06-11. A New S-Function Method searching for First Order Differential Integrals: Faster, Broader, Better. https://arxiv.org/abs/2306.06725

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