Zobrazeno 1 - 10
of 72
pro vyhledávání: '"da Mota, L. A. C. P."'
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 determining the Darboux polynomials of the vector field. In this arti
Externí odkaz:
http://arxiv.org/abs/2405.07912
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 Liouvillian first integral (belonging to a vast class of Liouvillian f
Externí odkaz:
http://arxiv.org/abs/2310.04850
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 established solid theoretical basis through a relation between the 1ODE we a
Externí odkaz:
http://arxiv.org/abs/2308.12391
Publikováno v:
Chaos, Solitons & Fractals Volume 177, December 2023, 114232
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 symmetries, dynamical symmetries and non-local symmetries) algorithmically.
Externí odkaz:
http://arxiv.org/abs/2306.13221
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 be seen as an improvement to the S-function method we have developed [
Externí odkaz:
http://arxiv.org/abs/2306.06725
Autor:
Duarte, L. G. S., da Mota, L. A. C. P.
Publikováno v:
Journal of Differential Equations Volume 300, 5 November 2021, Pages 356-385
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 Liouvillian first integral (or, equivalently, to rational first order d
Externí odkaz:
http://arxiv.org/abs/2004.09298
Autor:
Avellar, J., Duarte, L. G. S., Fraga, A., da Mota, L. A. C. P., de Oliveira, L. F., Pereira, L. O.
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 such systems is, therefore, an important topic of research. The present
Externí odkaz:
http://arxiv.org/abs/1811.11844
Autor:
Duarte, L. G. S., da Mota, L. A. C. P.
Publikováno v:
Computer Physics Communications Volume 254, September 2020, 107306
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 (rational 2ODEs) that are particularly `resistant' to canonical Lie methods
Externí odkaz:
http://arxiv.org/abs/1711.01646
Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background to deal, in
Externí odkaz:
http://arxiv.org/abs/1710.00674
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 provided an algorithm to find such Invariants. Here we introduce new theor
Externí odkaz:
http://arxiv.org/abs/1708.08893