Relevant bibliographies by topics / System of ordinary differential equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'System of ordinary differential equations'

Author: Grafiati
Published: 4 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "System of ordinary differential equations"

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Saltas, Vassilios, Vassilios Tsiantos, and Dimitrios Varveris. "Solving Differential Equations and Systems of Differential Equations with Inverse Laplace Transform." European Journal of Mathematics and Statistics 4, no. 3 (2023): 1–8. http://dx.doi.org/10.24018/ejmath.2023.4.3.192.

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The inverse Laplace transform enables the solution of ordinary linear differential equations as well as systems of ordinary linear differentials with applications in the physical and engineering sciences. The Laplace transform is essentially an integral transform which is introduced with the help of a suitable generalized integral. The ultimate goal of this work is to introduce the reader to some of the basic ideas and applications for solving initially ordinary differential equations and then systems of ordinary linear differential equations.
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Assanova, A. T., and Ye Shynarbek. "THE PARAMETER IDENTIFICATION PROBLEM FOR SYSTEM OF DIFFERENTIAL EQUATIONS." BULLETIN Series of Physics & Mathematical Sciences 73, no. 1 (2021): 7–13. http://dx.doi.org/10.51889/2021-1.1728-7901.01.

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In this paper, the parameter identification problem for system of ordinary differential equations is considered. The parameter identification problem for system of ordinary differential equations is investigated by the Dzhumabaev’s parametrization method. At first, conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations are obtained in the term of fundamental matrix of system’s differential part. Further, we establish conditions for a unique solvability of the parameter identification problem for system of ordinary differential
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Cai, Xin. "Numerical Simulation for the System of Ordinary Differential Equations." Advanced Materials Research 179-180 (January 2011): 37–42. http://dx.doi.org/10.4028/www.scientific.net/amr.179-180.37.

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Two coupled small parameter ordinary differential equations were considered. The solutions of differential equations will change rapidly near both sides of the boundary layer. Firstly, the properties were studied for differential equations. Secondly, the asymptotic properties of differential equations were discussed. Thirdly, the numerical methods with zero approximation were constructed for both left side and right side singular component differential equations. Finally, error analyses were given.
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Li, Xin, Chengli Zhao, Xue Zhang, and Xiaojun Duan. "Symbolic Neural Ordinary Differential Equations." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 17 (2025): 18511–19. https://doi.org/10.1609/aaai.v39i17.34037.

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Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great significance. In this study, we propose a novel learning framework of symbolic continuous-depth neural networks, termed Symbolic Neural Ordinary Differential Equations (SNODEs), to effectively and accurately learn the underlying dynamics of complex systems. Specifically, our learning framework comprises three stages: initially, pre-training a predefined symbolic neura
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Kosek, Zdeněk. "Nonlinear boundary value problem for a system of nonlinear ordinary differential equations." Časopis pro pěstování matematiky 110, no. 2 (1985): 130–44. http://dx.doi.org/10.21136/cpm.1985.108595.

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Ding, Zuohua, Hui Shen, and Qi-Wei Ge. "Checking system boundedness using ordinary differential equations." Information Sciences 187 (March 2012): 245–65. http://dx.doi.org/10.1016/j.ins.2011.10.018.

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Alabi, M. O., M. S. Olaleye, and K. S. Adewoye. "Initial Value Solvers for Direct Solution of Fourth Order Ordinary Differential Equations in a Block from Using Chebyshev Polynomial as Basis Function." International Journal of Mathematics and Statistics Studies 12, no. 2 (2024): 25–46. http://dx.doi.org/10.37745/ijmss.13/vol12n12546.

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The numerical computation of fourth order ordinary differential equations cannot be gloss over easily due to its significant and importance. There have been glowing needs to find an appropriate numerical method that will handle effectively fourth order ordinary differential equations without resolving such an equation to a system of first order ordinary differential equations. To this end, this presentation focuses on direct numerical computation to fourth order ordinary differential equations without resolving such equations to a system of first order ordinary differential equations. The meth
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Diblík, Josef. "The singular Cauchy-Nicoletti problem for the system of two ordinary differential equations." Mathematica Bohemica 117, no. 1 (1992): 55–67. http://dx.doi.org/10.21136/mb.1992.126234.

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Crow, John A. "A System of Ordinary Differential Equations (Gengzhe Chang)." SIAM Review 27, no. 3 (1985): 452–53. http://dx.doi.org/10.1137/1027120.

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Arguchintsev, Alexander, and Vasilisa Poplevko. "An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations." Games 12, no. 1 (2021): 23. http://dx.doi.org/10.3390/g12010023.

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This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optim
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Dissertations / Theses on the topic "System of ordinary differential equations"

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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.

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<p>In case of the PDE's the concept of solving by separation of variables</p><p>has a well defined meaning. One seeks a solution in a form of a</p><p>product or sum and tries to build the general solution out of these</p><p>particular solutions. There are also known systems of second order</p><p>ODE's describing potential motions and certain rigid bodies that are</p><p>considered to be separable. However, in those cases, the concept of</p><p>separation of variables is more elusive; no general definition is</p><p>given.</p><p>In this thesis we study how these systems of equations separate and f
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Kunze, Herbert Eduard. "Monotonicity properties of systems of ordinary differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21361.pdf.

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Tung, Michael Ming-Sha. "Spline approximations for systems of ordinary differential equations." Doctoral thesis, Universitat Politècnica de València, 2013. http://hdl.handle.net/10251/31658.

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El objetivo de esta tesis doctoral es desarrollar nuevos métodos basados en splines para la resolución de sistemas de ecuaciones diferenciales del tipo Y'(x)=f(x,Y(x)) , a<x<b Y(a)=Y_a (1) donde Y_a, Y(x) son matrices rxq, comenzando con splines de tipo cúbico y con un algoritmo similar al propuesto por Loscalzo y Talbot en el caso escalar [20], intentando poder aumentar el orden del spline, lo que con el método dado en [20] no puede hacerse de forma convergente. Trataremos también de aplicar dicho método al problema Y''(x)=f(x,Y(x),Y'(x)) , a<x<b Y(a)=Y_a Y'(a)=Y_b
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Hermansyah, Edy. "An investigation of collocation algorithms for solving boundary value problems system of ODEs." Thesis, University of Newcastle Upon Tyne, 2001. http://hdl.handle.net/10443/1976.

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This thesis is concerned with an investigation and evaluation of collocation algorithms for solving two-point boundary value problems for systems of ordinary differential equations. An emphasis is on developing reliable and efficient adaptive mesh selection algorithms in piecewise collocation methods. General background materials including basic concepts and descriptions of the method as well as some functional analysis tools needed in developing some error estimates are given at the beginning. A brief review of some developments in the methods to be used is provided for later referencing. By
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Caberlin, Martin D. "Stiff ordinary and delay differential equations in biological systems." Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=29416.

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The Santillan-Mackey model of the tryptophan operon was developed to characterize the anthranilate synthase activity in cultures of Escherichia coli. Similarly, the GABA reaction scheme was formulated to characterize the response of the GABAA receptor at a synapse, and the Hodgkin-Huxley model was developed to characterize the action potential of a squid giant axon. While the Hodgkin-Huxley model has been studied in great detail from a mathematical vantage, much less is known about the preceding two models in this regard. This work examines the stiffness of all three models; a novel perspectiv
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George, Daniel Pucknell. "Bifurcations and homoclinic orbits in piecewise linear ordinary differential equations." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233083.

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Khanamiryan, Marianna. "Numerical methods for systems of highly oscillatory ordinary differential equations." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/226323.

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This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential equations. Phenomena of high oscillation is considered a major computational problem occurring in Fourier analysis, computational harmonic analysis, quantum mechanics, electrodynamics and fluid dynamics. Classical methods based on Gaussian quadrature fail to approximate oscillatory integrals. In this work we introduce numerical methods which share the remarkable feature that the accuracy of approximation improves as the frequency of oscillation increas
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Neumann, Jens. "Consistency analysis of systems of partial and ordinary differential and algebraic equations." Thesis, Imperial College London, 2003. http://hdl.handle.net/10044/1/7717.

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Amir, Taher Kolar. "Comparison of numerical methods for solving a system of ordinary differential equations: accuracy, stability and efficiency." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48211.

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In this thesis, we compute approximate solutions to initial value problems of first-order linear ODEs using five explicit Runge-Kutta methods, namely the forward Euler method, Heun's method, RK4, RK5, and RK8. This thesis aims to compare the accuracy, stability, and efficiency properties of the five explicit Runge-Kutta methods. For accuracy, we carry out a convergence study to verify the convergence rate of the five explicit Runge-Kutta methods for solving a first-order linear ODE. For stability, we analyze the stability of the five explicit Runge-Kutta methods for solving a linear test equat
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Ospanov, Asset. "DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5674.

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Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic s
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Books on the topic "System of ordinary differential equations"

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Sideris, Thomas C. Ordinary Differential Equations and Dynamical Systems. Atlantis Press, 2013. http://dx.doi.org/10.2991/978-94-6239-021-8.

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Awrejcewicz, Jan. Ordinary Differential Equations and Mechanical Systems. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07659-1.

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F, Mishchenko E., and Matematicheskiĭ institut im. V.A. Steklova., eds. Topology, ordinary differential equations, dynamical systems. American Mathematical Society, 1986.

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Ilchmann, Achim. Surveys in Differential-Algebraic Equations I. Springer Berlin Heidelberg, 2013.

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V, Anosov D., and Arnolʹd V. I. 1937-, eds. Ordinary differential equations and smooth dynamical systems. Springer-Verlag, 1988.

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V, Anosov D., ed. Ordinary differential equations and smooth dynamical systems. Springer, 1997.

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Zhukova, Galina. Differential equations. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1072180.

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The textbook presents the theory of ordinary differential equations constituting the subject of the discipline "Differential equations". Studied topics: differential equations of first, second, arbitrary order; differential equations; integration of initial and boundary value problems; stability theory of solutions of differential equations and systems. Introduced the basic concepts, proven properties of differential equations and systems. The article presents methods of analysis and solutions. We consider the applications of the obtained results, which are illustrated on a large number of spe
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Maury, Bertrand. The Respiratory System in Equations. Springer Milan, 2013.

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Kogan, Efim. Ordinary differential equations and calculus of variations. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1058922.

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The textbook contains theoretical information in a volume of the lecture course are discussed in detail and examples of typical tasks and test tasks and tasks for independent work. &#x0D; Designed for students enrolled in directions of preparation 15.03.03 "Applied mechanics" 01.03.02 "mathematics" (specialization "Mathematical modeling"), major 23.05.01 "Land transport and technological means" (specialization "Dynamics and strength of transport and technological systems"). Can be used by teachers for conducting practical classes.
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Bosman, Stephen. Parameter estimation in systems of ordinary differential equations. University of Manchester, 1996.

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Book chapters on the topic "System of ordinary differential equations"

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Schechter, Martin. "Ordinary Differential Equations." In Minimax Systems and Critical Point Theory. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4902-9_4.

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Das, Malay Kumar, and Pradipta K. Panigrahi. "Ordinary Differential Equations." In Design and Analysis of Thermal Systems. CRC Press, 2023. http://dx.doi.org/10.1201/9781003049272-9.

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Papachristou, Costas J. "Ordinary Differential Equations." In Aspects of Integrability of Differential Systems and Fields. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-35002-4_3.

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Kuiry, Soumendra Nath, and Dhrubajyoti Sen. "Ordinary Differential Equations." In Modelling Hydrology, Hydraulics and Contaminant Transport Systems in Python. CRC Press, 2021. http://dx.doi.org/10.1201/9780429288579-3.

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Walter, Wolfgang. "Complex Linear Systems." In Ordinary Differential Equations. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0601-9_6.

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Henner, Victor, Alexander Nepomnyashchy, Tatyana Belozerova, and Mikhail Khenner. "Systems of Differential Equations." In Ordinary Differential Equations. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-25130-6_4.

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Shima, Hiroyuki, and Tsuneyoshi Nakayama. "System of Ordinary Differential Equations." In Higher Mathematics for Physics and Engineering. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/b138494_16.

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Adkins, William A., and Mark G. Davidson. "Linear Systems of Differential Equations." In Ordinary Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3618-8_9.

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Logemann, Hartmut, and Eugene P. Ryan. "Stability of Feedback Systems and Stabilization." In Ordinary Differential Equations. Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6398-5_6.

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Walter, Wolfgang. "First Order Systems. Equations of Higher Order." In Ordinary Differential Equations. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0601-9_4.

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Conference papers on the topic "System of ordinary differential equations"

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Shen, Zhan, and Kexin Li. "Analog Circuit for Solving Linear Ordinary Differential Equations." In 2024 IEEE 6th International Conference on Power, Intelligent Computing and Systems (ICPICS). IEEE, 2024. https://doi.org/10.1109/icpics62053.2024.10796335.

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Zhang, Shaorong, Koji Yamashita, and Nanpeng Yu. "Learning Power System Dynamics with Noisy Data Using Neural Ordinary Differential Equations." In 2024 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2024. http://dx.doi.org/10.1109/pesgm51994.2024.10689132.

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Bian, Hanlin, Wei Zhu, Zhang Chen, L. Jingsui, and Chao Pei. "Parameter Inversion of High-Dimensional Chaotic Systems Using Neural Ordinary Differential Equations." In 2024 IEEE 13th Data Driven Control and Learning Systems Conference (DDCLS). IEEE, 2024. http://dx.doi.org/10.1109/ddcls61622.2024.10606602.

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Li, Saiya, Litai Ma, Dehan Li, Yi Deng, Yi Yang, and Lei Xu. "A Robust Detection Network Utilizing Neural Memory Ordinary Differential Equations for Vertebral Fractures Diagnosis." In 2024 International Annual Conference on Complex Systems and Intelligent Science (CSIS-IAC). IEEE, 2024. https://doi.org/10.1109/csis-iac63491.2024.10919288.

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Bian, Hanlin, Wei Zhu, Zhang Chen, Jingsui Li, and Chao Pei. "Interpretable Fourier Neural Ordinary Differential Equations." In 2024 3rd Conference on Fully Actuated System Theory and Applications (FASTA). IEEE, 2024. http://dx.doi.org/10.1109/fasta61401.2024.10595255.

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Rahman, Aowabin, Jan Drgona, Aaron Tuor, and Jan Strube. "Neural Ordinary Differential Equations for Nonlinear System Identification." In 2022 American Control Conference (ACC). IEEE, 2022. http://dx.doi.org/10.23919/acc53348.2022.9867586.

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Feckan, Michal. "Transversal homoclinics in nonlinear systems of ordinary differential equations." In The 6'th Colloquium on the Qualitative Theory of Differential Equations. Bolyai Institute, SZTE, 1999. http://dx.doi.org/10.14232/ejqtde.1999.5.9.

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Steyer, Andrew, and Robert Kuether. "Connecting Functions of Nonlinear Ordinary Differential Equations." In Proposed for presentation at the SIAM Conference on Applications of Dynamical Systems held May 23-27, 2021 in Virtual. US DOE, 2021. http://dx.doi.org/10.2172/1870270.

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Nipp, Kaspar, Daniel Stoffer, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Mini-symposium: Ordinary Differential Equations and Dynamical Systems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241613.

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Wang, Mingqian, Jianshan Zhou, Xuting Duan, et al. "Nonlinear System Identification for Quadrotors with Neural Ordinary Differential Equations." In 2023 IEEE International Conference on Unmanned Systems (ICUS). IEEE, 2023. http://dx.doi.org/10.1109/icus58632.2023.10318403.

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Reports on the topic "System of ordinary differential equations"

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Moore, Peter K., and Linda R. Petzold. A Stepsize Control Strategy for Stiff Systems of Ordinary Differential Equations. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada281551.

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Lustman, Levi, and Beny Neta. Software for the Parallel Solution of Systems of Ordinary Differential Equations. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada235489.

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Landwehr, Philipp, Paulius Cebatarauskas, Csaba Rosztoczy, Santeri Röpelinen, and Maddalena Zanrosso. Inverse Methods In Freeform Optics. Technische Universität Dresden, 2023. http://dx.doi.org/10.25368/2023.148.

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Traditional methods in optical design like ray tracing suffer from slow convergence and are not constructive, i.e., each minimal perturbation of input parameters might lead to “chaotic” changes in the output. However, so-called inverse methods can be helpful in designing optical systems of reflectors and lenses. The equations in R2 become ordinary differential equations, while in R3 the equations become partial differential equations. These equations are then used to transform source distributions into target distributions, where the distributions are arbitrary, though assumed to be positive a
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Trahan, Corey, Jing-Ru Cheng, and Amanda Hines. ERDC-PT : a multidimensional particle tracking model. Engineer Research and Development Center (U.S.), 2023. http://dx.doi.org/10.21079/11681/48057.

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This report describes the technical engine details of the particle- and species-tracking software ERDC-PT. The development of ERDC-PT leveraged a legacy ERDC tracking model, “PT123,” developed by a civil works basic research project titled “Efficient Resolution of Complex Transport Phenomena Using Eulerian-Lagrangian Techniques” and in part by the System-Wide Water Resources Program. Given hydrodynamic velocities, ERDC-PT can track thousands of massless particles on 2D and 3D unstructured or converted structured meshes through distributed processing. At the time of this report, ERDC-PT support
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Knorrenschild, M. Differential-algebraic equations as stiff ordinary differential equations. Office of Scientific and Technical Information (OSTI), 1989. http://dx.doi.org/10.2172/6980335.

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Juang, Fen-Lien. Waveform methods for ordinary differential equations. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/5005850.

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Rivera-Casillas, Peter, and Ian Dettwiller. Neural Ordinary Differential Equations for rotorcraft aerodynamics. Engineer Research and Development Center (U.S.), 2024. http://dx.doi.org/10.21079/11681/48420.

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High-fidelity computational simulations of aerodynamics and structural dynamics on rotorcraft are essential for helicopter design, testing, and evaluation. These simulations usually entail a high computational cost even with modern high-performance computing resources. Reduced order models can significantly reduce the computational cost of simulating rotor revolutions. However, reduced order models are less accurate than traditional numerical modeling approaches, making them unsuitable for research and design purposes. This study explores the use of a new modified Neural Ordinary Differential
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Aslam, S., and C. W. Gear. Asynchronous integration of ordinary differential equations on multiprocessors. Office of Scientific and Technical Information (OSTI), 1989. http://dx.doi.org/10.2172/5979551.

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Dutt, Alok, Leslie Greengard, and Vladimir Rokhlin. Spectral Deferred Correction Methods for Ordinary Differential Equations. Defense Technical Information Center, 1998. http://dx.doi.org/10.21236/ada337779.

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Herzog, K. J., M. D. Morris, and T. J. Mitchell. Bayesian approximation of solutions to linear ordinary differential equations. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/6242347.

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