Literatura académica sobre el tema "Ordinary differential equations"
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Artículos de revistas sobre el tema "Ordinary differential equations"
Brauer, Fred, Vladimir I. Arnol'd y Roger Cook. "Ordinary Differential Equations." American Mathematical Monthly 100, n.º 8 (octubre de 1993): 810. http://dx.doi.org/10.2307/2324802.
Texto completoRawlins, A. D. y M. Sever. "Ordinary Differential Equations". Mathematical Gazette 72, n.º 462 (diciembre de 1988): 334. http://dx.doi.org/10.2307/3619967.
Texto completoKapadia, Devendra A. y V. I. Arnold. "Ordinary Differential Equations". Mathematical Gazette 79, n.º 484 (marzo de 1995): 228. http://dx.doi.org/10.2307/3620107.
Texto completoDory, Robert A. "Ordinary Differential Equations". Computers in Physics 3, n.º 5 (1989): 88. http://dx.doi.org/10.1063/1.4822872.
Texto completoLi, Haoxuan. "The advance of neural ordinary differential ordinary differential equations". Applied and Computational Engineering 6, n.º 1 (14 de junio de 2023): 1283–87. http://dx.doi.org/10.54254/2755-2721/6/20230709.
Texto completoSaltas, Vassilios, Vassilios Tsiantos y Dimitrios Varveris. "Solving Differential Equations and Systems of Differential Equations with Inverse Laplace Transform". European Journal of Mathematics and Statistics 4, n.º 3 (14 de junio de 2023): 1–8. http://dx.doi.org/10.24018/ejmath.2023.4.3.192.
Texto completoSanchez, David A. "Ordinary Differential Equations Texts." American Mathematical Monthly 105, n.º 4 (abril de 1998): 377. http://dx.doi.org/10.2307/2589736.
Texto completoIserles, A., D. W. Jordan y P. Smith. "Nonlinear Ordinary Differential Equations". Mathematical Gazette 72, n.º 460 (junio de 1988): 155. http://dx.doi.org/10.2307/3618957.
Texto completoSánchez, David A. "Ordinary Differential Equations Texts". American Mathematical Monthly 105, n.º 4 (abril de 1998): 377–83. http://dx.doi.org/10.1080/00029890.1998.12004897.
Texto completoHadeler, K. P. y S. Walcher. "Reducible Ordinary Differential Equations". Journal of Nonlinear Science 16, n.º 6 (29 de junio de 2006): 583–613. http://dx.doi.org/10.1007/s00332-004-0627-8.
Texto completoTesis sobre el tema "Ordinary differential equations"
MARINO, GISELA DORNELLES. "COMPLEX ORDINARY DIFFERENTIAL EQUATIONS". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10175@1.
Texto completoNeste texto estudamos diversos aspectos de singularidades de campos vetoriais holomorfos em dimensão 2. Discutimos detalhadamente o caso particular de uma singularidade sela-nó e o papel desempenhado pelas normalizações setoriais. Isto nos conduz à classificação analítica de difeomorfismos tangentes à identidade. seguir abordamos o Teorema de Seidenberg, tratando da redução de singularidades degeneradas em singularidades simples, através do procedimento de blow-up. Por fim, estudamos a demonstração do Teorema de Mattei-Moussu, acerca da existência de integrais primeiras para folheações holomorfas.
In the present text, we study the different aspects of singularities of holomorphic vector fields in dimension 2. We discuss in detail the particular case of a saddle-node singularity and the role of the sectorial normalizations. This leads us to the analytic classiffication of diffeomorphisms which are tangent to the identity. Next, we approach the Seidenberg Theorem, dealing with the reduction of degenerated singularities into simple ones, by means of the blow-up procedure. Finally, we study the proof of the well-known Mattei-Moussu Theorem concerning the existence of first integrals to holomorphic foliations.
Gehrs, Kai Frederik. "Algorithmic methods for ordinary differential equations". [S.l.] : [s.n.], 2006. http://ubdata.uni-paderborn.de/ediss/17/2007/gehrs.
Texto completoNg, Chee Loong. "Parameter estimation in ordinary differential equations". Texas A&M University, 2004. http://hdl.handle.net/1969.1/388.
Texto completoJorba, i. Monte Àngel. "On Quasiperiodic Perturbations of Ordinary Differential Equations". Doctoral thesis, Universitat de Barcelona, 1991. http://hdl.handle.net/10803/2122.
Texto completoIt is also known that, when the mass parameter "mi" (the mass of the small primary in the normalized units) is less than the Routh critical value "mi"(R) = 1/2(1 - square root (23/27) = 0.03852 ... (this is true in the Earth-Moon case) these points are linearly stable. Applying the KAM theorem to this case we can obtain that there exist invariant tori around these points. Now, if we restrict the motion of the particle to the plane of motion of the primaries we have that, inside each energy level, these tori split the phase space and this allows to prove that the equilateral points are stable (except for two values, "mi" = "mi"2 and "mi"= "mi"3 with low order resonances). In the spatial case, the invariant tori do not split the phase space and, due to the possible Arnold diffusion, these points can be unstable. But Arnold diffusion is a very slow phenomenon and we can have small neighbourhoods of "practical stability", that is, the particle will stay near the equilibrium point for very long time spans.
Unfortunately, the real Earth-Moon system is rather complex. In this case, due to the fact that that the motions of the Earth and the Moon are non circular (even non elliptical) and the strong influence of the Sun, the libration points do not exist as equilibrium points, and we need to define "instantaneous" libration points as the ones forming an equilateral triangle with the Earth and the Moon at each instant. If we perform some numerical integrations starting at (or near) these points we can see that the solutions go away after a short period of time, showing that these regions are unstable.
Two conclusions can be obtained from this fact. First: if we are interested in keeping a spacecraft there, we will need to use some kind of control. Second: the RTBP is not a good model for this problem} because the behaviour displayed by it is different from the one of the real system.
For these reasons, an improved model has been developed in order to study this problem. This model includes the main perturbations (due to the solar effect and to the noncircular motion of the Moon), assuming that they are quasi-periodic. This is a very good approximation for time spans of some thousands of years. It is not clear if this is true for longer time spans, but this matter will not be considered in this work. This model is in good agreement with the vector field of the solar system directly computed by means of the JPL ephemeris, for the time interval for which the JPL model is available.
The study of this kind of models is the main purpose of this work.
First of all, we have focused our attention on linear differential equations with constant coefficients, affected by a small quasi-periodic perturbation. These equations appear as variational equations along a quasi-periodic solution of a general equation and they also serve as an introduction to nonlinear problems.
The purpose is to reduce those systems to constant coefficients ones by means of a quasi-periodic change of variables, as the classical Floquet theorem does for periodic systems. It is also interesting to nave a way to compute this constant matrix, as well as the change of variables. The most interesting case occurs when the unperturbed system is of elliptic type. Other cases, as the hyperbolic one, have already been studied. We have added a parameter ("epsilon") in the system, multiplying the perturbation, such that if "epsilon" is equal to zero we recover the unperturbed system. In this case we have found that, under suitable hypothesis of non-resonance, analyticity and non-degeneracy with respect to "epsilon", it is possible to reduce the system to constant coefficients, for a cantorian set of values of "epsilon". Moreover, the proof is constructive in an iterative way. This means that it is possible to find approximations to the reduced matrix as well as to the change of variables that performs such reduction. These results are given in Chapter 1.
The nonlinear case is now going to be studied. We have then considered an elliptic equilibrium point of an autonomous ordinary differential equation, and we have added a small quasi-periodic perturbation, in such a way that the equilibrium point does not longer exist. As in the linear case, we have put a parameter ("epsilon") multiplying the perturbation. There is some "practical" evidence that there exists a quasi-periodic orbit, having the same basic frequencies that the perturbation, such that, when the perturbation goes to zero, this orbit goes to the equilibrium point. Our results show that, under suitable hypothesis, this orbit exists for a cantorian set of values of "epsilon". We have also found some results related to the stability of this orbit. These results are given in Chapter 2.
A remarkable case occurs when the system is Hamiltonian. Here it is interesting to know what happens to the invariant tori near these points when the perturbation is added. Note that the KAM theorem can not be applied directly due to the fact that the Hamiltonian is degenerated, in the sense that it has some frequencies (the ones of the perturbation) that have fixed values and they do not depend on actions in a diffeomorphic way. In this case, we have found that some tori still exist in the perturbed system. These tori come from the ones of the unperturbed system whose frequencies are non-resonant with those of the perturbation. The perturbed tori add these perturbing frequencies to the ones they already had. This can be described saying that the unperturbed tori are "quasi-periodically dancing" under the "rhythm" of the perturbation. These results can also be found in Chapter 2 and Appendix C.
The final point of this work has been to perform a study of the behaviour near the instantaneous equilateral libration points of the real Earth-Moon system. The purpose of those computations has been to find a way of keeping a spacecraft near these points in an unexpensive way. As it has been mentioned above in the real system these points are not equilibrium points, and their neighbourhood displays unstability. This leads us to use some control to keep the spacecraft there. It would be useful to have an orbit that was always near these points, because the spacecraft could be placed on it. Thus, only a station keeping would be necessary. The simplest orbit of this kind that we can compute is the one that replaces the equilibrium point. In Chapter 3, this computation has been carried out first for a planar simplified model and then for a spatial model. Then, the solution found for this last model has been improved, by means of numerical methods, in order to have a real orbit of the real system (here, by real system we mean the model of solar system provided by the JPL tapes). This improvement has been performed for a given (fixed) time-span. That is sufficient for practical purposes. Finally, an approximation to the linear stability of this refined orbit has been computed, and a very mild unstability has been found, allowing for an unexpensive station keeping. These results are given in Chapter 3 and Appendix A.
Finally, in Appendix B the reader can find the technical details concerning the way of obtaining the models used to study the neighbourhood of the equilateral points. This has been jointly developed with Gerard Gomez, Jaume Llibre, Regina Martinez, Josep Masdemont and Carles Simó.
We study several topics concerning quasi-periodic time-dependent perturbations of ordinary differential equations. This kind of equations appear in many applied problems of Celestial Mechanics, and we have used, as an illustration, the study of the behaviour near the Lagrangian points of the real Earth-Moon system. For this purpose, a model has been developed. It includes the main perturbations (due to the Sun and Moon), assuming that they are quasi-periodic.
Firstly, we deal with linear differential equations with constant coefficients, affected by a small quasi-periodic perturbation, trying to reduce then: to constant coefficients by means of a quasi-periodic change of variables. The most interesting case occurs when the unperturbed system is of elliptic type. We have added a parameter "epsilon" in the system, multiplying the perturbation, such that if "epsilon" is equal to zero we recover the unperturbed system. In this case, under suitable hypothesis of non-resonance, analyicity and non degeneracy with respect to "epsilon", it is possible to reduce the system to constant coefficients, for a cantorian set of values of "epsilon".
In the nonlinear case, we have considered an elliptic equilibrium point of an autonomous differential equation, and we have added a small quasi-periodic perturbation, in such a way that the equilibrium point does not exist. As in the linear case, we have put a parameter ("epsilon") multiplying the perturbation. Then, for a cantorian set of "epsilon", there exists a quasi-periodic orbit having the same basic frequencies as the perturbation, going to the equilibrium point when t: goes to zero. Some results concerning the stability of this orbit are stated. When the system is Hamiltonian, we have found that some tori still exist in the perturbed system. These tori come from the ones of the unperturbed system whose frequencies are non-resonant with those of the perturbation, adding these perturbing frequencies to the ones they already had.
Finally, a study of the behaviour near the Lagrangian points of the real Earth-Moon system is presented. The purpose has been to find the orbit replacing the equilibrium point. This computation has been carried out first for the model mentioned above and then it has been improved numerically, in order to have a real orbit of the real system. Finally, a study of the linear stability of this refined orbit has been done.
Måhl, Anna. "Separation of variables for ordinary differential equations". Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5620.
Texto completoIn case of the PDE's the concept of solving by separation of variables
has a well defined meaning. One seeks a solution in a form of a
product or sum and tries to build the general solution out of these
particular solutions. There are also known systems of second order
ODE's describing potential motions and certain rigid bodies that are
considered to be separable. However, in those cases, the concept of
separation of variables is more elusive; no general definition is
given.
In this thesis we study how these systems of equations separate and find that their separation usually can be reduced to sequential separation of single first order ODE´s. However, it appears that other mechanisms of separability are possible.
Lagrange, John. "Power Series Solutions to Ordinary Differential Equations". TopSCHOLAR®, 2001. http://digitalcommons.wku.edu/theses/672.
Texto completoSharples, Nicholas. "Some problems in irregular ordinary differential equations". Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55877/.
Texto completoHemmi, Mohamed Ali Carleton University Dissertation Mathematics and statistics. "Series solutions of nonlinear ordinary differential equations". Ottawa, 1994.
Buscar texto completoMaclean, John. "Numerical multiscale methods for ordinary differential equations". Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/12818.
Texto completoSaravi, Masoud. "Numerical solution of linear ordinary differential equations and differential-algebraic equations by spectral methods". Thesis, Open University, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446280.
Texto completoLibros sobre el tema "Ordinary differential equations"
Wolfgang, Walter. Ordinary differential equations. New York: Springer, 1998.
Buscar texto completoAdkins, William A. y Mark G. Davidson. Ordinary Differential Equations. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3618-8.
Texto completoWalter, Wolfgang. Ordinary Differential Equations. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0601-9.
Texto completoLogemann, Hartmut y Eugene P. Ryan. Ordinary Differential Equations. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6398-5.
Texto completoTahir-Kheli, Raza. Ordinary Differential Equations. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76406-1.
Texto completoPetrovski, I. G. Ordinary differential equations. London: Dover, 1985.
Buscar texto completoKrasnov, M. L. Ordinary differential equations. Moscow: Mir Publishers, 1987.
Buscar texto completo1932-, Rota Gian-Carlo, ed. Ordinary differential equations. 4a ed. New York: Wiley, 1989.
Buscar texto completoKrasnov, M. L. Ordinary differential equations. Moscow: Mir, 1987.
Buscar texto completoAdkins, William A. Ordinary Differential Equations. New York, NY: Springer New York, 2012.
Buscar texto completoCapítulos de libros sobre el tema "Ordinary differential equations"
Seifert, Christian, Sascha Trostorff y Marcus Waurick. "Ordinary Differential Equations". En Evolutionary Equations, 51–66. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89397-2_4.
Texto completoTahir-Kheli, Raza. "Differential Operator". En Ordinary Differential Equations, 1–4. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76406-1_1.
Texto completoStoer, J. y R. Bulirsch. "Ordinary Differential Equations". En Introduction to Numerical Analysis, 428–569. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-2272-7_7.
Texto completoVesely, Franz J. "Ordinary Differential Equations". En Computational Physics, 97–135. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-2307-6_4.
Texto completoShakarchi, Rami. "Ordinary Differential Equations". En Problems and Solutions for Undergraduate Analysis, 327–35. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1738-1_20.
Texto completoVesely, Franz J. "Ordinary Differential Equations". En Computational Physics, 89–123. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1329-2_4.
Texto completoKolmogorov, A. N. y A. P. Yushkevich. "Ordinary Differential Equations". En Mathematics of the 19th Century, 83–196. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8851-6_2.
Texto completoWoodford, C. y C. Phillips. "Ordinary Differential Equations". En Numerical Methods with Worked Examples: Matlab Edition, 197–214. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-1366-6_9.
Texto completoMotreanu, Dumitru, Viorica Venera Motreanu y Nikolaos Papageorgiou. "Ordinary Differential Equations". En Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 271–302. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_10.
Texto completoKomornik, Vilmos. "Ordinary Differential Equations". En Springer Undergraduate Mathematics Series, 141–63. London: Springer London, 2017. http://dx.doi.org/10.1007/978-1-4471-7316-8_6.
Texto completoActas de conferencias sobre el tema "Ordinary differential equations"
Bronstein, Manuel. "Linear ordinary differential equations". En Papers from the international symposium. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/143242.143264.
Texto completoBournez, Olivier. "Ordinary Differential Equations & Computability". En 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2018. http://dx.doi.org/10.1109/synasc.2018.00011.
Texto completoCID, J. ÁNGEL y RODRIGO L. POUSO. "EXISTENCE RESULTS FOR DISCONTINUOUS ORDINARY DIFFERENTIAL EQUATIONS". En Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0026.
Texto completoDamasceno, Berenice C. y Luciano Barbanti. "Ordinary fractional differential equations are in fact usual entire ordinary differential equations on time scales". En 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4904589.
Texto completoJankowski, Tadeusz, Theodore E. Simos, George Psihoyios y Ch Tsitouras. "Ordinary Differential Equations with Deviated Arguments". En Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790130.
Texto completoBiyar, Magzhan. "Degenerate operators for ordinary differential equations". En INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5049018.
Texto completoBian, Hanlin, Wei Zhu, Zhang Chen, Jingsui Li y Chao Pei. "Interpretable Fourier Neural Ordinary Differential Equations". En 2024 3rd Conference on Fully Actuated System Theory and Applications (FASTA). IEEE, 2024. http://dx.doi.org/10.1109/fasta61401.2024.10595255.
Texto completoRAMIS, JEAN-PIERRE. "GEVREY ASYMPTOTICS AND APPLICATIONS TO HOLOMORPHIC ORDINARY DIFFERENTIAL EQUATIONS". En Differential Equations & Asymptotic Theory in Mathematical Physics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702395_0002.
Texto completoTsarev, S. P. "On factorization of nonlinear ordinary differential equations". En the 1999 international symposium. New York, New York, USA: ACM Press, 1999. http://dx.doi.org/10.1145/309831.309899.
Texto completoTEIXEIRA, M. A. y P. R. DA SILVA. "SINGULAR PERTURBATION FOR DISCONTINUOUS ORDINARY DIFFERENTIAL EQUATIONS". En Proceedings of the International Conference on SPT 2007. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812776174_0023.
Texto completoInformes sobre el tema "Ordinary differential equations"
Knorrenschild, M. Differential-algebraic equations as stiff ordinary differential equations. Office of Scientific and Technical Information (OSTI), mayo de 1989. http://dx.doi.org/10.2172/6980335.
Texto completoJuang, Fen-Lien. Waveform methods for ordinary differential equations. Office of Scientific and Technical Information (OSTI), enero de 1990. http://dx.doi.org/10.2172/5005850.
Texto completoRivera-Casillas, Peter y Ian Dettwiller. Neural Ordinary Differential Equations for rotorcraft aerodynamics. Engineer Research and Development Center (U.S.), abril de 2024. http://dx.doi.org/10.21079/11681/48420.
Texto completoAslam, S. y C. W. Gear. Asynchronous integration of ordinary differential equations on multiprocessors. Office of Scientific and Technical Information (OSTI), julio de 1989. http://dx.doi.org/10.2172/5979551.
Texto completoDutt, Alok, Leslie Greengard y Vladimir Rokhlin. Spectral Deferred Correction Methods for Ordinary Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, enero de 1998. http://dx.doi.org/10.21236/ada337779.
Texto completoOber, Curtis C., Roscoe Bartlett, Todd S. Coffey y Roger P. Pawlowski. Rythmos: Solution and Analysis Package for Differential-Algebraic and Ordinary-Differential Equations. Office of Scientific and Technical Information (OSTI), febrero de 2017. http://dx.doi.org/10.2172/1364461.
Texto completoHerzog, K. J., M. D. Morris y T. J. Mitchell. Bayesian approximation of solutions to linear ordinary differential equations. Office of Scientific and Technical Information (OSTI), noviembre de 1990. http://dx.doi.org/10.2172/6242347.
Texto completoGrebogi, C. y J. A. Yorke. Chaotic transients, higher dimensional phenomena, and coupled ordinary differential equations. Office of Scientific and Technical Information (OSTI), enero de 1990. http://dx.doi.org/10.2172/5008774.
Texto completoHereman, Willy y Sigurd Angenent. The Painleve Test for Nonlinear Ordinary and Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, enero de 1989. http://dx.doi.org/10.21236/ada212894.
Texto completoLee, Kookjin y Eric Parish. Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems. Office of Scientific and Technical Information (OSTI), octubre de 2020. http://dx.doi.org/10.2172/1706214.
Texto completo