Author
M. S. Cardoso
Bio: M. S. Cardoso is an academic researcher from Rio de Janeiro State University. The author has contributed to research in topics: Ordinary differential equation & Symbolic computation. The author has an hindex of 1, co-authored 2 publications receiving 4 citations.
Papers
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TL;DR: A new approach to search for first order invariants (first integrals) of rational second order ordinary differential equations, an alternative to the Darbouxian and symmetry approaches, which can succeed in many cases where these two approaches fail.
6 citations
TL;DR: A semi-algorithm to find Liouvillian first integrals of dynamical systems in the plane based on a Darboux-type procedure to find the integrating factor for the system.
4 citations
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TL;DR: In this article, a method to solve a family of third-order nonlinear ordinary complex differential equations (NLOCDEs) by generalizing Prelle-Singer has been developed.
Abstract: A method to solve a family of third-order nonlinear ordinary complex differential equations (NLOCDEs) —nonlinear ODEs in the complex plane—by generalizing Prelle–Singer has been developed. The approach that the authors generalized is a procedure of obtaining a solution to a kind of second-order nonlinear ODEs in the real line. Some theoretical work has been illustrated and applied to several examples. Also, an extended technique of generating second and third motion integrals in the complex domain has been introduced, which is conceptually an analog to the motion in the real line. Moreover, the procedures of the method mentioned above have been verified.
1 citations
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TL;DR: In this article, the integrability analysis of a 3D system of first order rational differential equations (1ODEs) with free parameters has been studied in the context of finding elementary invariants.
Abstract: 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 theoretical results that will lead to a novel, more efficient, approach to determine these invariants. Furthermore, one important aspect of such dynamical systems is that the integrability can be an issue. We will show that the present theoretical development allows for an Integrability analysis in the case where the system has free parameters.
1 citations
TL;DR: In this paper, a generalized S -function method for rational second-order ordinary differential equations (2ODEs) has been proposed, which is able to deal with a class of 2ODEs that are resistant to canonical Lie methods and to Darbouxian approaches.
1 citations
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TL;DR: A new approach to deal with first order ordinary differential equations (1ODEs), presenting functions is presented, an alternative to the one presented in [1], and the theoretical background to deal, in the extended Prelle-Singer approach context, with systems of 1ODEs is established.
Abstract: 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 the extended Prelle-Singer approach context, with systems of 1ODEs. In this present paper, we will apply these results in order to produce a method that is more efficient in a great number of cases. Directly, the solving of 1ODEs is applicable to any problem presenting parameters to which the rate of change is related to the parameter itself. Apart from that, the solving of 1ODEs can be a part of larger mathematical processes vital to dealing with many problems.