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Relevant bibliographies by topics / Methods of ordinary differential equations

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

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2025

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

1

Askarova, A., Ye. Gripp, and G. Yeleussizova. "NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS." Scientific heritage, no. 103 (December 21, 2022): 67–69. https://doi.org/10.5281/zenodo.7467608.

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For many applied problems it is practically impossible to obtain the exact solution of differential equations. In these cases, methods of approximate solution of differential equations are used. This article considers the solution of a differential equation by various numerical methods.

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Jankowski, Tadeusz. "One-step methods for ordinary differential equations with parameters." Applications of Mathematics 35, no. 1 (1990): 67–83. http://dx.doi.org/10.21136/am.1990.104388.

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AM, K. SELV. "Alternative Methods of Ordinary Differential Equations." International Journal of Mathematics Trends and Technology 54, no. 6 (2018): 448–53. http://dx.doi.org/10.14445/22315373/ijmtt-v54p554.

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Ramos, J. I. "Linearized methods for ordinary differential equations." Applied Mathematics and Computation 104, no. 2-3 (1999): 109–29. http://dx.doi.org/10.1016/s0096-3003(98)10056-5.

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Gear, C. W. "Parallel methods for ordinary differential equations." Calcolo 25, no. 1-2 (1988): 1–20. http://dx.doi.org/10.1007/bf02575744.

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Li, Haoxuan. "The advance of neural ordinary differential ordinary differential equations." Applied and Computational Engineering 6, no. 1 (2023): 1283–87. http://dx.doi.org/10.54254/2755-2721/6/20230709.

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Differential methods are widely used to describe complex continuous processes. The main idea of ordinary differential equations is to treat a specific type of neural network as a discrete equation. Therefore, the differential equation solver can be used to optimize the solution process of the neural network. Compared with the conventional neural network solution, the solution process of the neural ordinary differential equation has the advantages of high storage efficiency and adaptive calculation. This paper first gives a brief review of the residual network (ResNet) and the relationship of R

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Shintani, Hisayoshi. "Two-step methods for ordinary differential equations." Hiroshima Mathematical Journal 14, no. 3 (1985): 471–78. http://dx.doi.org/10.32917/hmj/1206132929.

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Butcher, John. "General linear methods for ordinary differential equations." Mathematics and Computers in Simulation 79, no. 6 (2009): 1834–45. http://dx.doi.org/10.1016/j.matcom.2007.02.006.

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Tranquilli, Paul, and Adrian Sandu. "Exponential-Krylov methods for ordinary differential equations." Journal of Computational Physics 278 (December 2014): 31–46. http://dx.doi.org/10.1016/j.jcp.2014.08.013.

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Ramos, J. I., та C. M. García-López. "Linearized Θ-methods I. Ordinary differential equations". Computer Methods in Applied Mechanics and Engineering 129, № 3 (1996): 255–69. http://dx.doi.org/10.1016/0045-7825(95)00915-9.

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Dissertations / Theses on the topic "Methods of ordinary differential equations"

1

Gehrs, Kai Frederik. "Algorithmic methods for ordinary differential equations." [S.l.] : [s.n.], 2006. http://ubdata.uni-paderborn.de/ediss/17/2007/gehrs.

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Maclean, John. "Numerical multiscale methods for ordinary differential equations." Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/12818.

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This thesis is concerned with a class of explicit numerical methods for multiscale differential equations, including the Heterogeneous Multiscale Methods (HMM) and Projective Integration (PI) methods. These techniques have been developed within the last decade and successfully applied to a wide range of multiscale problems. We examine the HMM and PI methods when applied to multiscale systems for which the dynamics converges rapidly to a lower dimensional manifold defined in terms of the slow degrees of freedom, and provide rigorous convergence results for the methods under these conditions. Th

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Zhang, Quanju. "Ordinary differential equation methods for some optimization problems." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/710.

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Saravi, 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.

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This thesis involves the implementation of spectral methods, for numerical solution of linear Ordinary Differential Equations (ODEs) and linear Differential-Algebraic Equations (DAEs). First we consider ODEs with some ordinary problems, and then, focus on those problems in which the solution function or some coefficient functions have singularities. Then, by expressing weak and strong aspects of spectral methods to solve these kinds of problems, a modified pseudospectral method which is more efficient than other spectral methods is suggested and tested on some examples. We extend the pseudo-sp

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Brown, A. A. "Optimisation methods involving the solution of ordinary differential equations." Thesis, University of Hertfordshire, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374887.

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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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Walker, Matthew Thomas. "Theta Methods For Nonlinear Ordinary Differential Equations and Error Analysis." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/theses/1495.

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AN ABSTRACT OF THE THESIS OF Matthew Walker, for the Master of Science degree in Mathematics, presented on July 3, 2014, at Southern Illinois University Carbondale. TITLE: THETA METHODS OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS AND ERROR ANALYSIS MAJOR PROFESSOR: Dr. H. Schurz This paper will discuss how Theta Methods applied to a Nonlinear Ordinary Differential Equation behave for different critical values of theta. We will look at the stability, consistency, and convergence of the Forward Euler Method, Backward Euler Method, Trapezoidal Method, and the Midpoint Method. All of which can be

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Niesen, Jitse. "On the global error of discretization methods for ordinary differential equations." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616182.

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Patrulescu, Flavius-Olimpiu. "Ordinary differential equations and contact problems : modeling, analysis and numerical methods." Perpignan, 2012. http://www.theses.fr/2012PERP1284.

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Ce manuscrit est divisé en deux parties et huit chapitres. La première partie contient les chapitres 1-3 et présente des résultats concernant les méthodes numériques pour le problème de Cauchy associé aux équations différentielles ordinaires. La deuxième partie se réfère à la modélisation et l'analyse de quelques problèmes de contact sans frottement pour les matériaux élastiques ou viscoélastiques linéaire. Elle contient les chapitres 4-8. Dans la première partie de la thèse on introduit quelques méthodes numériques de type Runge-Kutta. Pour ces méthodes on obtient des résultats nouveaux conce

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Rana, Muhammad Sohel. "Analysis and Implementation of Numerical Methods for Solving Ordinary Differential Equations." TopSCHOLAR®, 2017. https://digitalcommons.wku.edu/theses/2053.

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Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number

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Books on the topic "Methods of ordinary differential equations"

1

Ang, W. T. Ordinary differential equations: Methods and applications. Universal Publishers, 2008.

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Butcher, J. C. Numerical Methods for Ordinary Differential Equations. John Wiley & Sons, Ltd., 2008.

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Kuzmina, R. P. Asymptotic Methods for Ordinary Differential Equations. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9347-2.

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Fitzpatrick, Patrick, Mario Martelli, Jean Mawhin, and Roger Nussbaum. Topological Methods for Ordinary Differential Equations. Edited by Massimo Furi and Pietro Zecca. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0085073.

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Bellen, Alfredo, Charles W. Gear, and Elvira Russo, eds. Numerical Methods for Ordinary Differential Equations. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0089227.

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Butcher, J. C. Numerical Methods for Ordinary Differential Equations. John Wiley & Sons, Ltd, 2016. http://dx.doi.org/10.1002/9781119121534.

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Butcher, J. C. Numerical Methods for Ordinary Differential Equations. John Wiley & Sons, Ltd, 2003. http://dx.doi.org/10.1002/0470868279.

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Griffiths, David F., and Desmond J. Higham. Numerical Methods for Ordinary Differential Equations. Springer London, 2010. http://dx.doi.org/10.1007/978-0-85729-148-6.

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Butcher, J. C. Numerical methods for ordinary differential equations. Wiley, 2008.

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10

Gear, C. William. Parallel methods for ordinary differential equations. Department of Computer Science, University of Illinois at Urbana-Champaign, 1987.

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

1

Adkins, William A., and Mark G. Davidson. "Power Series Methods." In Ordinary Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3618-8_7.

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Li, PhD, Haksun. "Ordinary Differential Equations." In Numerical Methods Using Kotlin. Apress, 2022. http://dx.doi.org/10.1007/978-1-4842-8826-9_7.

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Pagonis, Vasilis, and Christopher W. Kulp. "Ordinary Differential Equations." In Mathematical Methods using Python. CRC Press, 2024. http://dx.doi.org/10.1201/9781003294320-10.

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Lebl, Jiří. "Ordinary Differential Equations." In Methods in Molecular Biology. Humana Press, 2012. http://dx.doi.org/10.1007/978-1-62703-059-5_20.

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Li, PhD, Haksun. "Ordinary Differential Equations." In Numerical Methods Using Java. Apress, 2022. http://dx.doi.org/10.1007/978-1-4842-6797-4_7.

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Angheluta, Luiza. "Ordinary Differential Equations." In Analytical Methods in Physics. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-77053-1_3.

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Durran, Dale R. "Ordinary Differential Equations." In Numerical Methods for Fluid Dynamics. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6412-0_2.

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Simonovits, András. "Ordinary Differential Equations." In Mathematical Methods in Dynamic Economics. Palgrave Macmillan UK, 2000. http://dx.doi.org/10.1057/9780230513532_6.

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Antia, H. M. "Ordinary Differential Equations." In Numerical Methods for Scientists and Engineers. Hindustan Book Agency, 2012. http://dx.doi.org/10.1007/978-93-86279-52-1_12.

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Potter, Merle C., and Brian F. Feeny. "Ordinary Differential Equations." In Mathematical Methods for Engineering and Science. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-26151-0_1.

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

1

Olanrewaju, A. F., S. E. Fadugba, T. G. Shaba, and O. J. Akinremi. "Continuous Two-Step Block Methods for Solving Special Third Order of Ordinary Differential Equations." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10630235.

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Singh, Soumyendra, Shaik Atheeq Rasool, and R. Prasanna Kumar. "Solving Ordinary Differential Equations Using Custom Loss Convolutional Neural Network Method." In 2023 IEEE International Conference on Cloud Computing in Emerging Markets (CCEM). IEEE, 2023. http://dx.doi.org/10.1109/ccem60455.2023.00016.

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Otonritse, Okoro Joshua, Taiwo Omotayo Adebayo, Babatunde Olufemi Adebesin, Odetunde Olutunde Samuel, and Hassan Mumuni Olanrewaju. "Numerical Soluion of Singular Initial Value Problems in Ordinary Differential Equations by Iterative Decomposition and Bernstein Polynomial Methods." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10630284.

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Nayyeri, Mojtaba, Chengjin Xu, Franca Hoffmann, Mirza Mohtashim Alam, Jens Lehmann, and Sahar Vahdati. "Knowledge Graph Representation Learning using Ordinary Differential Equations." In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. Association for Computational Linguistics, 2021. http://dx.doi.org/10.18653/v1/2021.emnlp-main.750.

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Liang, Yuxuan, Kun Ouyang, Hanshu Yan, Yiwei Wang, Zekun Tong, and Roger Zimmermann. "Modeling Trajectories with Neural Ordinary Differential Equations." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/207.

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Recent advances in location-acquisition techniques have generated massive spatial trajectory data. Recurrent Neural Networks (RNNs) are modern tools for modeling such trajectory data. After revisiting RNN-based methods for trajectory modeling, we expose two common critical drawbacks in the existing uses. First, RNNs are discrete-time models that only update the hidden states upon the arrival of new observations, which makes them an awkward fit for learning real-world trajectories with continuous-time dynamics. Second, real-world trajectories are never perfectly accurate due to unexpected senso

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Mendes, Fábio Mace^do. "Bayesian inference in the numerical solution of ordinary differential equations." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP, 2013. http://dx.doi.org/10.1063/1.4819993.

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Kang, Xinyu, Siyu Wang, Jichang Zeng, and Yuxuan Zhao. "Forward Euler method for ordinary differential equations." In International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), edited by Ke Chen, Nan Lin, Romeo Meštrović, Teresa A. Oliveira, Fengjie Cen, and Hong-Ming Yin. SPIE, 2022. http://dx.doi.org/10.1117/12.2628078.

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Bucharskyi, Valeriy. "BACKWARD NORDSIECK’S METHODS FOR NUMERICAL SOLVING OF ORDINARY DIFFERENTIAL EQUATIONS." In MODALITĂȚI CONCEPTUALE DE DEZVOLTARE A ȘTIINȚEI MODERNE. European Scientific Platform, 2020. http://dx.doi.org/10.36074/20.11.2020.v5.25.

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MOIR, N. "A NEW CLASS OF METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS." In Proceedings of the International Conference (ICCMSE 2003). WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704658_0094.

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Barkatou, Moulay A. "Symbolic methods for solving systems of linear ordinary differential equations." In the 2010 International Symposium. ACM Press, 2010. http://dx.doi.org/10.1145/1837934.1837940.

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Reports on the topic "Methods of ordinary differential equations"

1

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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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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Werner, L., and F. Odeh. Numerical Methods for Stiff Ordinary and Elliptic Partial Differential Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada153247.

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4

Van Wieren, Jack. Using Diagonally Implicit Multistage Integration Methods for Solving Ordinary Differential Equations. Part 2: Implicit Methods. Defense Technical Information Center, 1997. http://dx.doi.org/10.21236/ada328947.

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VanWieren, Jack. Using Diagonally Implicit Multistage Integration Methods for Solving Ordinary Differential Equations. Part 1: Introduction and Explicit Methods. Defense Technical Information Center, 1997. http://dx.doi.org/10.21236/ada324085.

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6

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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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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