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Relevant bibliographies by topics / Ordinary fourth-order differential equations

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Academic literature on the topic 'Ordinary fourth-order differential equations'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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Journal articles on the topic "Ordinary fourth-order differential equations"

1

Tóthová, Mária, and Oleg Palumbíny. "On monotone solutions of the fourth order ordinary differential equations." Czechoslovak Mathematical Journal 45, no. 4 (1995): 737–46. http://dx.doi.org/10.21136/cmj.1995.128553.

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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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3

Ma, Ruyun, and Fengran Zhang. "POSITIVE SOLUTIONS OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS." Acta Mathematica Scientia 18 (October 1998): 124–28. http://dx.doi.org/10.1016/s0252-9602(17)30886-x.

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4

Ashyralyev, Allaberen, and Ibrahim Mohammed Ibrahım. "High-Order, Accurate Finite Difference Schemes for Fourth-Order Differential Equations." Axioms 13, no. 2 (2024): 90. http://dx.doi.org/10.3390/axioms13020090.

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This article is devoted to the study of high-order, accurate difference schemes’ numerical solutions of local and non-local problems for ordinary differential equations of the fourth order. Local and non-local problems for ordinary differential equations with constant coefficients can be solved by classical integral transform methods. However, these classical methods can be used simply in the case when the differential equation has constant coefficients. We study fourth-order differential equations with dependent coefficients and their corresponding boundary value problems. Novel compact numer

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Jrad, Fahd, and Uğurhan Muğan. "Non-polynomial Fourth Order Equations which Pass the Painlevé Test." Zeitschrift für Naturforschung A 60, no. 6 (2005): 387–400. http://dx.doi.org/10.1515/zna-2005-0601.

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The singular point analysis of fourth order ordinary differential equations in the non-polynomial class are presented. Some new fourth order ordinary differential equations which pass the Painlevé test as well as the known ones are found. -PACS: 02.30.Hq, 02.30.Ik, 02.30.Gp

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Kamo, K. I., and H. Usami. "Oscillation theorems for fourth-order quasilinear ordinary differential equations." Studia Scientiarum Mathematicarum Hungarica 39, no. 3-4 (2002): 385–406. http://dx.doi.org/10.1556/sscmath.39.2002.3-4.10.

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7

Przybycin, Jolanta. "Nonlinear eigenvalue problems for fourth order ordinary differential equations." Annales Polonici Mathematici 60, no. 3 (1995): 249–53. http://dx.doi.org/10.4064/ap-60-3-249-253.

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Kudryashov, Nicolai A. "Transcendents defined by nonlinear fourth-order ordinary differential equations." Journal of Physics A: Mathematical and General 32, no. 6 (1999): 999–1013. http://dx.doi.org/10.1088/0305-4470/32/6/012.

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Korman, Philip. "A maximum principle for fourth order ordinary differential equations." Applicable Analysis 33, no. 3-4 (1989): 267–73. http://dx.doi.org/10.1080/00036818908839878.

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Palumbíny, Oleg. "On oscillatory solutions of fourth order ordinary differential equations." Czechoslovak Mathematical Journal 49, no. 4 (1999): 779–90. http://dx.doi.org/10.1023/a:1022401101007.

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Dissertations / Theses on the topic "Ordinary fourth-order differential equations"

1

Woods, Patrick Daniel. "Localisation in reversible fourth-order ordinary differential equations." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299269.

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Jenab, Bita. "Asymptotic theory of second-order nonlinear ordinary differential equations." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/24690.

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The asymptotic behaviour of nonoscillatory solutions of second order nonlinear ordinary differential equations is studied. Necessary and sufficient conditions are given for the existence of positive solutions with specified asymptotic behaviour at infinity. Existence of nonoscillatory solutions is established using the Schauder-Tychonoff fixed point theorem. Techniques such as factorization of linear disconjugate operators are employed to reveal the similar nature of asymptotic solutions of nonlinear differential equations to that of linear equations. Some examples illustrating the asymptoti

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3

Sun, Xun. "Twin solutions of even order boundary value problems for ordinary differential equations and finite difference equations." [Huntington, WV : Marshall University Libraries], 2009. http://www.marshall.edu/etd/descript.asp?ref=1014.

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Boutayeb, Abdesslam. "Numerical methods for high-order ordinary differential equations with applications to eigenvalue problems." Thesis, Brunel University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.278244.

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Esposito, Elena. "Numerical treatment of special second order ordinary differential equations: general and exponentially fitted methods." Doctoral thesis, Universita degli studi di Salerno, 2012. http://hdl.handle.net/10556/292.

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2010 - 2011<br>The aim of this research is the construction and the analysis of new families of numerical methods for the integration of special second order Ordinary Differential Equations (ODEs). The modeling of continuous time dynamical systems using second order ODEs is widely used in many elds of applications, as celestial mechanics, seismology, molecular dynamics, or in the semidiscretisation of partial differential equations (which leads to high dimensional systems and stiffness). Although the numerical treatment of this problem has been widely discussed in the literature, the in

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Gray, Michael Jeffery Henderson Johnny L. "Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations." Waco, Tex. : Baylor University, 2006. http://hdl.handle.net/2104/4185.

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Koike, Tatsuya. "On the exact WKB analysis of second order linear ordinary differential equations with simple poles." 京都大学 (Kyoto University), 2000. http://hdl.handle.net/2433/181093.

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Granström, Frida. "Symmetry methods and some nonlinear differential equations : Background and illustrative examples." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-48020.

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Differential equations, in particular the nonlinear ones, are commonly used in formulating most of the fundamental laws of nature as well as many technological problems, among others. This makes the need for methods in finding closed form solutions to such equations all-important. In this thesis we study Lie symmetry methods for some nonlinear ordinary differential equations (ODE). The study focuses on identifying and using the underlying symmetries of the given first order nonlinear ordinary differential equation. An extension of the method to higher order ODE is also discussed. Several illus

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Shu, Yupeng. "Numerical Solutions of Generalized Burgers' Equations for Some Incompressible Non-Newtonian Fluids." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2051.

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The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\vare

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Yaakub, Abdul Razak Bin. "Computer solution of non-linear integration formula for solving initial value problems." Thesis, Loughborough University, 1996. https://dspace.lboro.ac.uk/2134/25381.

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This thesis is concerned with the numerical solutions of initial value problems with ordinary differential equations and covers single step integration methods. focus is to study the numerical the various aspects of Specifically, its main methods of non-linear integration formula with a variety of means based on the Contraharmonic mean (C.M) (Evans and Yaakub [1995]), the Centroidal mean (C.M) (Yaakub and Evans [1995]) and the Root-Mean-Square (RMS) (Yaakub and Evans [1993]) for solving initial value problems. the applications of the second It includes a study of order C.M method for parallel

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Books on the topic "Ordinary fourth-order differential equations"

1

Bonheure, Denis. Heteroclinic solutions for a class of fourth order ordinary differential equations. Académie royale de Belgique, Classe des Sciences, 2006.

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2

Paris, R. B. Asymptotics of high-order ordinary differential equations. Pitman Advanced, 1985.

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3

D, Wood A., ed. Asymptotics of high-order ordinary differential equations. Pitman Pub., 1986.

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4

David, Freed Alan, and Lewis Research Center, eds. Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations. Lewis Research Center, 1991.

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5

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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Boutayeb, Abdesslam. Numerical methods for high-order ordinary differential equations with applications to eigenvalue problems. Brunel University, 1990.

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7

Takashi, Aoki, and Kyōto Daigaku. Sūri Kaiseki Kenkyūjo., eds. Virtual truning points and bifurcation of Stokes curves for higher order ordinary differential equations. Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2004.

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8

N, Phillips Timothy, and Institute for Computer Applications in Science and Engineering., eds. Pseudospectral collocation methods for fourth order differential equations. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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9

Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Book chapters on the topic "Ordinary fourth-order differential equations"

1

Ragab, Saad A., and Hassan E. Fayed. "Fourth-Order Ordinary Differential Equations." In Introduction to Finite Element Analysis for Engineers, 2nd ed. CRC Press, 2024. http://dx.doi.org/10.1201/9781003323150-3.

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2

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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Henner, Victor, Alexander Nepomnyashchy, Tatyana Belozerova, and Mikhail Khenner. "First-Order Differential Equations." In Ordinary Differential Equations. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-25130-6_2.

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Adkins, William A., and Mark G. Davidson. "First Order Differential Equations." In Ordinary Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3618-8_1.

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Adkins, William A., and Mark G. Davidson. "Second Order Linear Differential Equations." In Ordinary Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3618-8_5.

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Walter, Wolfgang. "First Order Equations: Some Integrable Cases." In Ordinary Differential Equations. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0601-9_2.

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Walter, Wolfgang. "Theory of First Order Differential Equations." In Ordinary Differential Equations. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0601-9_3.

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Henner, Victor, Alexander Nepomnyashchy, Tatyana Belozerova, and Mikhail Khenner. "Differential Equations of Order n > 1." In Ordinary Differential Equations. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-25130-6_3.

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9

Henner, Victor, Alexander Nepomnyashchy, Tatyana Belozerova, and Mikhail Khenner. "Boundary-Value Problems for Second-Order ODEs." In Ordinary Differential Equations. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-25130-6_9.

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Adkins, William A., and Mark G. Davidson. "Second Order Constant Coefficient Linear Differential Equations." In Ordinary Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3618-8_3.

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Conference papers on the topic "Ordinary fourth-order differential equations"

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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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Omole, Ezekiel Olaoluwa, Ogunware Bankola Gbenga, Florence Dami Ayegbusi, Peter Onu, Tosin Oreyeni, and Kehinde Peter Ajewole. "Hybrid Block Numerical Algorithm for Direct Solutions of Ordinary Differential Equations of the Third and Fourth Orders." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10629770.

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Matthew, David Adeleke, Emmanuel Oluseye Adeyefa, Ezekiel Olaoluwa Omole, and Kehinde Peter Ajewole. "A Model of a Single Numerical Method for the Integration of Multi-order 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/seb4sdg60871.2024.10629993.

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Takács, Donát M., and Tamás Fülöp. "Improving Discrete Numerical Methods for Dynamics Using Continuous Mathematical Tools." In 10th International Scientific Conference on Advances in Mechanical Engineering. Trans Tech Publications Ltd, 2025. https://doi.org/10.4028/p-11tto6.

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We briefly review backward error analysis as a useful mathematical technique for improving numerical methods used for solving ordinary differential equations describing dynamical systems. Then, we show how backward error analysis-based compensation, an approach recently introduced by the authors, can be applied to the second-order Newmark method for eliminating numerical damping and achieving fourth-order convergence. The presented improvements only require modifying the physical parameters of the system and the excitation, while the Newmark method is left intact. We compare the performance of

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Ogunware, Bankola Gbenga, Ezekiel Olaoluwa Omole, Adefunke Bosede Familua, et al. "Solving Ordinary Differential Equations of First and Second Order Using a Single Numerical Algorithm with Four Equidistant Points." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10629726.

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Samat, Faieza, and Fudziah Ismail. "Fourth-order explicit hybrid method for solving special second-order ordinary differential equations." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801123.

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Jikantoro, Yusuf Dauda, Fudziah Ismail, and Noraz Senu. "A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801239.

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BONHEURE, D., J. M. GOMES, and L. SANCHEZ. "POSITIVE SOLUTIONS OF A SECOND ORDER SINGULAR ORDINARY DIFFERENTIAL EQUATION." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0028.

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Schwarz, Fritz. "Janet bases of 2nd order ordinary differential equations." In the 1996 international symposium. ACM Press, 1996. http://dx.doi.org/10.1145/236869.240354.

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Zainuddin, Nooraini, and Zarina Bibi Ibrahim. "Block method for third order ordinary differential equations." In PROCEEDINGS OF THE 24TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Mathematical Sciences Exploration for the Universal Preservation. Author(s), 2017. http://dx.doi.org/10.1063/1.4995919.

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Reports on the topic "Ordinary fourth-order differential equations"

1

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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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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Greer, John B., Andrea L. Bertozzi, and Guillermo Sapiro. Fourth Order Partial Differential Equations on General Geometries. Defense Technical Information Center, 2005. http://dx.doi.org/10.21236/ada524786.

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