57 citations · 163 across the 21 of their papers we have counts for
10 papers · 1 filter
A Linear Prelle-Singer method
L. G. S. Duarte, H. S. Ferreira, L. A. C. P. da Mota
The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of…
Solving first order differential equations presenting elementary functions
L. G. S. Duarte, L. A. C. P. da Mota, A. B. M. M. Queiroz
We have already dealt with the problem of solving First Order Differential Equations (1ODEs) presenting elementary functions before in [1, 2]. In this present paper, we have establ…
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
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…
An Efficient Method for Computing Liouvillian First Integrals of Planar Polynomial Vector Fields
L. G. S. Duarte, L. A. C. P. da Mota
Here we present an efficient method to compute Darboux polynomials for polynomial vector fields in the plane. This approach is restricetd to polynomial vector fields presenting a L…
A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator
L. G. S. Duarte, L. A. C. P. da Mota
In [1,2] we have developed a method (we call it the S-function method) that is successful in treating certain classes of rational second order ordinary differential equations (rati…
Dealing with Rational Second Order Ordinary Differential Equations where both Darboux and Lie Find It Difficult: The -function Method
J. Avellar, M. S. Cardoso, L. G. S. Duarte +1
Here we present a new approach to search for first order invariants (first integrals) of rational second order ordinary differential equations. This method is an alternative to the…
A Semi-Algorithmic Search for Lie Symmetries
L. G. S. Duarte, L. A. C. P. da Mota
In [Solving second order ordinary differential equations by extending the Prelle-Singer method, J. Phys. A: Math.Gen., 34, 3015-3024 (2001)] we defined a function (we called S) ass…
Determining Liouvillian First Integrals for Dynamical Systems in the Plane
J. Avellar, L. G. S. Duarte, S. E. S. Duarte +1
Here we present/implement an algorithm to find Liouvillian first integrals of dynamical systems in the plane. In \cite{JCAM}, we have introduced the basis for the present implement…
A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II
L. G. S. Duarte, S. E. S. Duarte, L. A. C. P. da Mota
We present a semi-decision procedure to tackle first order differential equations, with Liouvillian functions in the solution (LFOODEs). As in the case of the Prelle-Singer procedu…
A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution
L. G. S. Duarte, S. E. S. Duarte, L. A. C. P. da Mota
We present an algorithm to solve First Order Ordinary Differential Equations (FOODEs) extending the Prelle-Singer (PS) Method. The usual PS-approach miss many FOODEs presenting Lio…