57 citations · 164 across the 25 of their papers we have counts for
15 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…
The search for Invariants for 3D Systems of 1ODEs - a new Method and Integrability Analysis
L. G. S. Duarte, J. P. C. Eiras, L. A. C. P. da Mota
In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also prov…