57 citations · 164 across the 25 of their papers we have counts for
25 papers
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…
A new use of nonlocal symmetries for computing Liouvillian first integrals of rational second order ordinary differential equations
I. Deme, L. G. S. Duarte, L. A. C. P. da Mota
Here we present an efficient method for finding and using a nonlocal symmetry admitted by a rational second order ordinary differential equation (rational 2ODE) in order to find a…
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…
Finding nonlocal Lie symmetries algorithmically
L. G. S. Duarte, L. A. C. P. da Mota, A. F. Rocha
Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmet…
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…