57 citations · 163 across the 21 of their papers we have counts for
22 papers
The S-function at arbitrary order: hyperplanes of symmetries and the realisability condition
L. G. S. Duarte, L. A. C. P. da Mota
For a scalar equation the -function of the extended Prelle--Singer method is a vector , the null-form vector of Chandrase…
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…
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…
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…
Solving 1ODEs with functions
L. G. S. Duarte, L. A. C. P. da Mota, A. B. M. M. Queiroz
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…
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…
Numerical Calculation With Arbitrary Precision
B. O. Rodrigues, L. A. C. P. da Mota, L. G. S. Duarte
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited…
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…
Implementation of the Prelle-Singer Method for 1ODEs
L. G. S. Duarte, S. E. S. Duarte, L. A. C. P. da Mota +1
A set of MapleV R5 software routines for solving first order ordinary differential equations (1ODEs) is presented. The package implements the Prelle-Singer Method in its original f…
Numerical Calculations Using Maple: Why & How?
E. V. Correa Silva, L. G. S. Duarte, L. A. C. P. da Mota +1
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studyin…
Numerical Analysis of Dynamical Systems and the Fractal Dimension of Boundaries
L. G. S. Duarte, L. A. C. P. da Mota, H. P. de Oliveira +2
A set of MapleV R.4/5 software routines for calculating the numerical evolution of dynamical systems and flexibly plotting the results is presented. The package consists of an init…
Computer Algebra Solving of Second Order ODEs Using Symmetry Methods
E. S. Cheb-Terrab, L. G. S. Duarte, L. A. C. P. da Mota
An update of the ODEtools Maple package, for the analytical solving of 1st and 2nd order ODEs using Lie group symmetry methods, is presented. The set of routines includes an ODE-so…
Computer Algebra Solving of First Order ODEs Using Symmetry Methods
E. S. Cheb-Terrab, L. G. S. Duarte, L. A. C. P. da Mota
A set of Maple V R.3/4 computer algebra routines for the analytical solving of 1st. order ODEs, using Lie group symmetry methods, is presented. The set of commands includes a 1st.…
Patterns of quark mass matrices in a class of Calabi-Yau models
F. del Aguila, M. Masip, L. da Mota
We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete -singlet sector, which has been…