Relevant bibliographies by topics / Methods of ordinary differential equations / Dissertations / Theses
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Dissertations / Theses on the topic 'Methods of ordinary differential equations'

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Published: 4 June 2021
Last updated: 28 July 2025

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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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2

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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3

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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4

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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6

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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7

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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8

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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9

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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10

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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11

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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12

Hoskins, Jeremy G. "The application of symmetry methods and conservation laws to ordinary differential equations and a linear wave equation." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/43321.

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Symmetry analysis and conservation laws are widely used in analyzing and solving differential equations. Conservation laws are also called first integrals when dealing with ordinary differential equations (ODEs). In this thesis, the complementary nature of these two approaches is explored; specifically, the use of symmetries to find integrating factors and, conversely, the use of conservation laws to seek new symmetries. In Part 1, building upon results in [3] and [10], it is shown that a higher-order symmetries of an ODE induces a point symmetry of the corresponding integrating factor determi
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13

Krueger, Justin Michael. "Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/78674.

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The compositions of in-host microbial communities (microbiota) play a significant role in host health, and a better understanding of the microbiota's role in a host's transition from health to disease or vice versa could lead to novel medical treatments. One of the first steps toward this understanding is modeling interaction dynamics of the microbiota, which can be exceedingly challenging given the complexity of the dynamics and difficulties in collecting sufficient data. Methods such as principal differential analysis, dynamic flux estimation, and others have been developed to overcome these
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14

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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15

Clairon, Quentin. "New regularization methods for the inverse problem of parameter estimation in Ordinary differential equations." Thesis, Evry-Val d'Essonne, 2015. http://www.theses.fr/2015EVRY0024/document.

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Nous présentons dans cette thèse deux méthodes de régularisation du problème d’estimationde paramètres dans des équations différentielles ordinaires (EDOs). La première est une extensionde la méthode two-step, permettant d’obtenir une expression de la variance asymptotique etd’éviter l’usage de la derivée de l’estimateur non-paramétrique. Elle fait appel à la notion desolution faible et propose une caractérisation variationnelle de la solution de l’EDO. Ce faisant,elle identifie le vrai ensemble de paramètres comme celui respectant un ensemble de moments,fonctions plus régulières des paramètre
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16

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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17

Hovhannisyan, A. H., and Bert-Wolfgang Schulze. "On a method for solution of the ordinary differential equations connected with Huygens' equations." Universität Potsdam, 2010. http://opus.kobv.de/ubp/volltexte/2010/4538/.

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18

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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19

Dozier, Zijun Lan. "Modeling the hydrolyzing action of secretory phospholipase A2 with ordinary differential equations and Monte Carlo Methods." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2398.pdf.

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20

Xia, Xiaoyue. "New asymptotic methods for the global analysis of ordinary differential equations and for non-selfadjoint spectral problems." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437062908.

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21

Calatayud, Gregori Julia. "Computational methods for random differential equations: probability density function and estimation of the parameters." Doctoral thesis, Universitat Politècnica de València, 2020. http://hdl.handle.net/10251/138396.

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[EN] Mathematical models based on deterministic differential equations do not take into account the inherent uncertainty of the physical phenomenon (in a wide sense) under study. In addition, inaccuracies in the collected data often arise due to errors in the measurements. It thus becomes necessary to treat the input parameters of the model as random quantities, in the form of random variables or stochastic processes. This gives rise to the study of random ordinary and partial differential equations. The computation of the probability density function of the stochastic solution is important
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22

Hahne, Jan [Verfasser]. "Waveform-relaxation methods for ordinary and stochastic differential equations with applications in distributed neural network simulations / Jan Hahne." Wuppertal : Universitätsbibliothek Wuppertal, 2018. http://d-nb.info/1164103385/34.

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23

Al-Harbi, Saleh M. "Implicit Runge-Kutta methods for the numerical solution of stiff ordinary differential equation." Thesis, University of Manchester, 1999. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.488322.

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The primary aim of this thesis is to calculate the numerical solution of a given stiff system of ordinary differential equations. We deal with the implementation of the implicit Runge-Kutta methods, in particular for Radau IIA order 5 which is now a competitive method for solving stiff initial value problems. New software based on Radau IIA, called IRKMR5 written in MATLAB has been developed for fixed order (order 5) with variable stepsizes, which is quite efficient when it is used to solve stiff problems. The code is organized in a modular form so that it facilitates both the understanding of
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24

Bossio, Castro Alvaro Manuel. "Lagrangeovský model pohybu kavitační bubliny." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401546.

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In this thesis, the dynamics of an isolated cavitation bubble submerged in a steady flow is studied numerically. A Lagrangian-Eulerian approach is considered, in which properties of the fluid are computed first by means of Eulerian methods (in this study the commercial CFD software Ansys Fluent 19 was used) and the trajectory of the bubble is then computed in a Lagrangian fashion, i.e. the bubble is considered as a small particle moving relative to the fluid, due to the effect of several forces depending on fluid's pressure field, fluid's velocity field and bubble's radius. Bubble's radius dyn
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25

Janssen, Micha. "A Constraint Satisfaction Approach for Enclosing Solutions to Initial Value Problems for Parametric Ordinary Differential Equations." Université catholique de Louvain, 2001. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-11042002-155822/.

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This work considers initial value problems (IVPs) for ordinary differential equations (ODEs) where some of the data is uncertain and given by intervals as is the case in many areas of science and engineering. Interval methods provide a way to approach these problems but they raise fundamental challenges in obtaining high accuracy and low computation costs. This work introduces a constraint satisfaction approach to these problems which enhances traditional interval methods with a pruning step based on a global relaxation of the ODE. The relaxation uses Hermite interpolation polynomials and encl
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26

Xie, Chunmei. "An efficient method for the calculation of the free-surface Green function using ordinary differential equations." Thesis, Ecole centrale de Nantes, 2019. http://www.theses.fr/2019ECDN0013/document.

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Le calcul des efforts hydrodynamiques de premier ordre sur un ou plusieurs corps perçant la surface libre est aujourd'hui bien maîtrisé, et plusieurs codes de calcul implémentant la méthode des singularités (dite BEM ou méthode d'élément frontière) ont été développés. Le cadre est la théorie linéarisée des écoulements potentiels à une surface libre. Dans ces codes BEM, les singularités utilisées ont la propriété intrinsèque de satisfaire à la fois l'équation de Laplace dans le domaine fluide ainsi que la condition linéarisée de surface libre. Ces singularités, dites fonctions de Green à surfac
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27

Fels, Mark Eric. "Some applications of Cartan's method of equivalence to the geometric study of ordinary and partial differential equations." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41274.

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Cartan's method of equivalence is used to prove that there exists two fundamental tensorial invariants which determine the geometry of systems of n ($ ge$ 2) second order ordinary differential equations. These invariants allow us prove that there exist a unique equivalence class of second order equations which admit a Lie point symmetry group of maximal dimension, the dimension being $n sp2 + 4n + 3$. For third order systems of ordinary differential equations, we prove that the possible dimension of the point symmetry group is bounded by $n sp2 + 3n + 3$. As well we find that there is a unique
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28

Mayo, Colin F. "Implementation of the Runge-Kutta-Fehlberg method for solution of ordinary differential equations on a parallel processor." Thesis, Monterey, California. Naval Postgraduate School, 1987. http://hdl.handle.net/10945/22285.

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29

Asai, Yusuke [Verfasser], Peter E. [Akademischer Betreuer] Kloeden, and Andreas [Akademischer Betreuer] Neuenkirch. "Numerical methods for random ordinary differential equations and their applications in biology and medicine / Yusuke Asai. Gutachter: Peter E. Kloeden ; Andreas Neuenkirch." Frankfurt am Main : Universitätsbibliothek Johann Christian Senckenberg, 2016. http://d-nb.info/1100523782/34.

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30

Barbarroux, Loïc. "Contributions à la modélisation multi-échelles de la réponse immunitaire T-CD8 : construction, analyse, simulation et calibration de modèles." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEC026/document.

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Lors de l’infection par un pathogène intracellulaire, l’organisme déclenche une réponse immunitaire spécifique dont les acteurs principaux sont les lymphocytes T-CD8. Ces cellules sont responsables de l’éradication de ce type d’infections et de la constitution du répertoire immunitaire de l’individu. Les processus qui composent la réponse immunitaire se répartissent sur plusieurs échelles physiques inter-connectées (échelle intracellulaire, échelle d’une cellule, échelle de la population de cellules). La réponse immunitaire est donc un processus complexe, pour lequel il est difficile d’observe
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31

Lee, Hock Seng, and n/a. "An ODE/MOL PDE Template For Soil Physics: A Numerical Study." Griffith University. Australian School of Environmental Studies, 2003. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20030616.142709.

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The aim of the thesis is to find a method, in conjunction with the ordinary differential equation (ODE) based method of lines (MOL) solution of Richards’ equation, to model the steep wetting front infiltration in very dry soils, accurately and efficiently. Due to the steep pressure head or steep water volumetric content gradients, highly nonlinear soil hydraulic properties and the rapid movement of the wetting front, accurate solutions for infiltration into a dry soil are usually difficult to obtain. Additionally, such problems often require very small time steps and large computation times. A
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Lee, Hock Seng. "An ODE/MOL PDE Template For Soil Physics." Thesis, Griffith University, 2003. http://hdl.handle.net/10072/365588.

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The aim of the thesis is to find a method, in conjunction with the ordinary differential equation (ODE) based method of lines (MOL) solution of Richards’ equation, to model the steep wetting front infiltration in very dry soils, accurately and efficiently. Due to the steep pressure head or steep water volumetric content gradients, highly nonlinear soil hydraulic properties and the rapid movement of the wetting front, accurate solutions for infiltration into a dry soil are usually difficult to obtain. Additionally, such problems often require very small time steps and large computation times. A
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33

Stapor, Paul [Verfasser], Jan [Akademischer Betreuer] Hasenauer, Matthias [Gutachter] Chung, Wilhelm [Gutachter] Huisinga, and Jan [Gutachter] Hasenauer. "Efficient computational methods for parameter estimation of ordinary differential equation and mixed-effect models in systems biology / Paul Stapor ; Gutachter: Matthias Chung, Wilhelm Huisinga, Jan Hasenauer ; Betreuer: Jan Hasenauer." München : Universitätsbibliothek der TU München, 2021. http://d-nb.info/1234149087/34.

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34

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.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Neste 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,
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35

Ronan, Andrew S. "Analytic and Numerical Studies of a Simple Model of Attractive-Repulsive Swarms." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/11.

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We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model
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Nečasová, Gabriela. "Paralelní numerické řešení parciálních diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-236119.

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This thesis deals with the topic of partial differential equations parallel solutions. First, it focuses on ordinary differential equations (ODE) and their solution methods using Taylor polynomial. Another part is devoted to partial differential equations (PDE). There are several types of PDE, there are parabolic, hyperbolic and eliptic PDE. There is also explained how to use TKSL system for PDE computing. Another part focuses on solution methods of PDE, these methods are forward, backward and combined methods. There was explained, how to solve these methods in TKSL and Matlab systems. Computi
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Santos, Karine de Almeida. "Teoria da média para equações diferenciais ordinárias e algumas aplicações em mecânica clássica." Universidade Federal de Uberlândia, 2016. https://repositorio.ufu.br/handle/123456789/16823.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The main objective of this dissertation is to establish the basic results of the Averaging Theory for Ordinary Differential Equations and used them in some problems of Classical Mechanics. Two mechanical problems are given here. The first one is about the existence and stability of periodic solutions in the mathematical pendulum with dissipation. The second one is about the existence of periodic solutions of regularized Hill lunar problem with comes from Celestial Mechanics<br>O principal objetivo desta dissertação é estabelecer re
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Robacker, Thomas C. "Comparison of Two Parameter Estimation Techniques for Stochastic Models." Digital Commons @ East Tennessee State University, 2015. https://dc.etsu.edu/etd/2567.

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Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often f
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Sales, Filho Nazime 1986. "Análise qualitativa de um modelo de propagação de dengue para populações espacialmente homogêneas." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306772.

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Orientador: Bianca Morelli Rodolfo Calsavara<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T15:10:31Z (GMT). No. of bitstreams: 1 SalesFilho_Nazime_M.pdf: 36937949 bytes, checksum: 4ceff2992bbc8648a89104715aac602e (MD5) Previous issue date: 2015<br>Resumo: Neste trabalho será analisado um modelo matemático que descreve a propagação da dengue. Tal modelo é dado por um sistema de equações diferenciais ordinárias não lineares sujeitas a condições iniciais, que desc
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Marano, Susan Aileen. "Smarticles: A Method for Identifying and Correcting Instability and Error Caused by Explicit Integration Techniques in Physically Based Simulations." DigitalCommons@CalPoly, 2014. https://digitalcommons.calpoly.edu/theses/1304.

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Using an explicit integration method in physically based animations has many advantages including conceptual and computational simplicity, however, it re- quires small time steps to ensure low numerical instability. Simulations with large numbers of individually interacting components such as cloth, hair, and fluid models, are limited by the sections of particles most susceptible to error. This results in the need for smaller time steps than required for the majority of the system. These sections can be diverse and dynamic, quickly changing in size and location based on forces in the system. I
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Ng, Chee Loong. "Parameter estimation in ordinary differential equations." Texas A&M University, 2004. http://hdl.handle.net/1969.1/388.

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The parameter estimation problem or the inverse problem of ordinary differential equations is prevalent in many process models in chemistry, molecular biology, control system design and many other engineering applications. It concerns the re-construction of auxillary parameters by fitting the solution from the system of ordinary differential equations( from a known mathematical model) to that of measured data obtained from observing the solution trajectory. Some of the traditional techniques (for example, initial value technques, multiple shooting, etc.) used to solve this class of problem ha
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42

Jorba, i. Monte Àngel. "On Quasiperiodic Perturbations of Ordinary Differential Equations." Doctoral thesis, Universitat de Barcelona, 1991. http://hdl.handle.net/10803/2122.

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In this work we study several topics concerning quasi-periodic time-dependent perturbations of ordinary differential equations. This kind of equations appear as models in many applied problems of Celestial Mechanics, and we have used, as an illustration, the study of the behaviour near the equilateral libration points of the real Earth-Moon system. Let us introduce this problem as a motivation. As a first approximation, suppose that the Earth and Moon arc revolving in circular orbits around their centre of masses, neglect the effect of the rest of the solar system and neglect the spherical ter
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43

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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Lagrange, John. "Power Series Solutions to Ordinary Differential Equations." TopSCHOLAR®, 2001. http://digitalcommons.wku.edu/theses/672.

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In this thesis, the reader will be made aware of methods for finding power series solutions to ordinary differential equations. In the case that a solution to a differential equation may not be expressed in terms of elementary functions, it is practical to obtain a solution in the form of an infinite series, since many differential equations which yield such a solution model an actual physical situation. In this thesis, we introduce conditions that guarantee existence and uniqueness of analytic solutions, both in the linear and nonlinear case. Several methods for obtaining analytic solutions a
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45

Sharples, Nicholas. "Some problems in irregular ordinary differential equations." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55877/.

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We study the non-autonomous ordinary differential equation x = f (t, x) in the situation when the vector field f is of limited regularity, typically belonging to a space LP (O,T; Lq (JRn)). Such equations arise naturally when switching from an Eulerian to a Lagrangian viewpoint for the solutions of partial differential equations. We discuss some measurability issues in the foundations of the theory of regular Lagrangian flow solutions. Further, we examine the sensitivity of the choice of representative vector field f on solutions of the ordinary differential equation and, in particular, we dem
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46

Hemmi, Mohamed Ali Carleton University Dissertation Mathematics and statistics. "Series solutions of nonlinear ordinary differential equations." Ottawa, 1994.

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47

Loch, Guilherme Galina. "Sistemas rígidos associados a cadeias de decaimento radioativo." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-25082016-221140/.

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Os progressos computacionais nas últimas décadas e a teoria matemática cada vez mais sólida têm possibilitado a resolução de problemas de alta complexidade, permitindo uma modelagem cada vez mais detalhada da realidade. Tal verdade aplica-se inclusive para os sistemas rígidos de Equações Diferencias Ordinárias (EDOs): existem métodos numéricos altamente performáticos para este tipo de problema, que permitem uma grande variação no tamanho do passo de integração sem impactar na sua convergência. Este trabalho apresenta um estudo sobre o conceito de rigidez e técnicas numéricas para resolução de
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48

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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49

Tam, Kim M. "ODEASY, a query tool for ordinary differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ36744.pdf.

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50

Carvalho, Alexandre Nolasco de. "Infinite dimensional dynamics described by ordinary differential equations." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/29585.

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