10 citations · 20 across the 5 of their papers we have counts for
5 papers
Associative Integrator
J. Avellar, L. G. S. Duarte, L. A. C. P. da Mota +1
Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of s…
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…
Improving a family of Darboux methods for rational second order ordinary differential equations
L. G. S. Duarte, L. A. C. P. da Mota
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mention…
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…
Finding Elementary First Integrals for Rational Second Order Ordinary Differential Equations
J. Avellar, L. G. S. Duarte, S. E. S. Duarte +1
Here we present an algorithm to find elementary first integrals of rational second order ordinary differential equations (SOODEs). In \cite{PS2}, we have presented the first algori…