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Prelle-Singer Method


The Prelle-Singer method is a semi-decision procedure for solving nonlinear first-order ordinary differential equations of the form y^'=P(x,y)/Q(x,y), where P and Q are polynomials. It is based on knowledge of the structure of the integrating factor, and requires the specification of degree bounds for polynomials in the integrating factor. Duarte et al. (2000) have extended the Prelle-Singer procedure to second-order ODEs of the form y^('')=P(x,y,y^')/Q(x,y,y^'), again with P and Q polynomials.


This entry contributed by Bhuvanesh Bhatt

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References

Duarte, L. G. S.; da Mota, L. A.; and Skea, J. E. F. "Solving Second Order Ordinary Differential Equations by Extending the PS Method." 3 Jan 2000. http://arxiv.org/abs/math-ph/0001004.Man, Y. K. and MacCallum, M. A. H. "A Rational Approach to the Prelle-Singer Algorithm." J. Symb. Comput. 24, 31-43, 1997.Prelle, M. and Singer, M. "Elementary First Integrals of Differential Equations." Trans. Amer. Math. Soc. 279, 215-229, 1983.Singer, M. "Liouvillian First Integrals of Differential Equations." Trans. Amer. Math. Soc. 333, 673-688, 1992.

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Prelle-Singer Method

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Bhatt, Bhuvanesh. "Prelle-Singer Method." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Prelle-SingerMethod.html

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