Дисертації з теми "Singularly Perturbed Differential Equation"
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Mbroh, Nana Adjoah. "On the method of lines for singularly perturbed partial differential equations." University of the Western Cape, 2017. http://hdl.handle.net/11394/5679.
Повний текст джерелаMany chemical and physical problems are mathematically described by partial differential equations (PDEs). These PDEs are often highly nonlinear and therefore have no closed form solutions. Thus, it is necessary to recourse to numerical approaches to determine suitable approximations to the solution of such equations. For solutions possessing sharp spatial transitions (such as boundary or interior layers), standard numerical methods have shown limitations as they fail to capture large gradients. The method of lines (MOL) is one of the numerical methods used to solve PDEs. It proceeds by the discretization of all but one dimension leading to systems of ordinary di erential equations. In the case of time-dependent PDEs, the MOL consists of discretizing the spatial derivatives only leaving the time variable continuous. The process results in a system to which a numerical method for initial value problems can be applied. In this project we consider various types of singularly perturbed time-dependent PDEs. For each type, using the MOL, the spatial dimensions will be discretized in many different ways following fitted numerical approaches. Each discretisation will be analysed for stability and convergence. Extensive experiments will be conducted to confirm the analyses.
Song, Xuefeng. "Dynamic modeling issues for power system applications." Texas A&M University, 2003. http://hdl.handle.net/1969.1/1591.
Повний текст джерелаIragi, Bakulikira. "On the numerical integration of singularly perturbed Volterra integro-differential equations." University of the Western Cape, 2017. http://hdl.handle.net/11394/5669.
Повний текст джерелаEfficient numerical approaches for parameter dependent problems have been an inter- esting subject to numerical analysts and engineers over the past decades. This is due to the prominent role that these problems play in modeling many real life situations in applied sciences. Often, the choice and the e ciency of the approaches depend on the nature of the problem to solve. In this work, we consider the general linear first-order singularly perturbed Volterra integro-differential equations (SPVIDEs). These singularly perturbed problems (SPPs) are governed by integro-differential equations in which the derivative term is multiplied by a small parameter, known as "perturbation parameter". It is known that when this perturbation parameter approaches zero, the solution undergoes fast transitions across narrow regions of the domain (termed boundary or interior layer) thus affecting the convergence of the standard numerical methods. Therefore one often seeks for numerical approaches which preserve stability for all the values of the perturbation parameter, that is "numerical methods. This work seeks to investigate some "numerical methods that have been used to solve SPVIDEs. It also proposes alternative ones. The various numerical methods are composed of a fitted finite difference scheme used along with suitably chosen interpolating quadrature rules. For each method investigated or designed, we analyse its stability and convergence. Finally, numerical computations are carried out on some test examples to con rm the robustness and competitiveness of the proposed methods.
Davis, Paige N. "Localised structures in some non-standard, singularly perturbed partial differential equations." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/201835/1/Paige_Davis_Thesis.pdf.
Повний текст джерелаAdkins, Jacob. "A Robust Numerical Method for a Singularly Perturbed Nonlinear Initial Value Problem." Kent State University Honors College / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1513331499579714.
Повний текст джерелаHöhne, Katharina. "Analysis and numerics of the singularly perturbed Oseen equations." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-188322.
Повний текст джерелаReibiger, Christian. "Optimal Control Problems with Singularly Perturbed Differential Equations as Side Constraints: Analysis and Numerics." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-162862.
Повний текст джерелаKaiser, Klaus [Verfasser], Sebastian [Akademischer Betreuer] Noelle, Jochen [Akademischer Betreuer] Schütz, and Claus-Dieter [Akademischer Betreuer] Munz. "A high order discretization technique for singularly perturbed differential equations / Klaus Kaiser ; Sebastian Noelle, Jochen Schütz, Claus-Dieter Munz." Aachen : Universitätsbibliothek der RWTH Aachen, 2018. http://d-nb.info/1187251372/34.
Повний текст джерелаReibiger, Christian [Verfasser], Hans-Görg [Akademischer Betreuer] Roos, and Gert [Akademischer Betreuer] Lube. "Optimal Control Problems with Singularly Perturbed Differential Equations as Side Constraints: Analysis and Numerics / Christian Reibiger. Gutachter: Hans-Görg Roos ; Gert Lube. Betreuer: Hans-Görg Roos." Dresden : Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://d-nb.info/106909658X/34.
Повний текст джерелаRoos, Hans-Görg, and Martin Schopf. "Layer structure and the galerkin finite element method for a system of weakly coupled singularly perturbed convection-diffusion equations with multiple scales." Cambridge University Press, 2015. https://tud.qucosa.de/id/qucosa%3A39046.
Повний текст джерелаGordon, Brandon W. (Brandon William). "State space modeling of differential-algebraic systems using singularly perturbed sliding manifolds." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/9340.
Повний текст джерелаIncludes bibliographical references (p. 126-128).
This thesis introduces a new approach for modeling and control of algebraically constrained dynamic systems. The formulation of dynamic systems in terms of differential equations ·and algebraic constraints provides a systematic framework that is well suited for object oriented modeling of thermo-fluid systems. In this approach, differential equations are used to describe the evolution of subsystem states and algebraic equations are used to define the interconnections between the subsystems (boundary conditions). Algebraic constraints also commonly occur as a result of modeling simplifications such as steady state approximation of fast dynamics and rigid body assumptions that result in kinematic constraints. Important examples of algebraically constrained dynamic systems include multi-body problems, chemical processes, and two phase thermo-fluid systems. Differential-algebraic equation (DAE) systems often referred to as descriptor, implicit, or singular systems present a number of difficult problems in simulation and control. One of the key difficulties is that DAEs are not expressed in an explicit state space form required by many simulation and control design methods. This is particularly true in control of nonlinear DAE systems for which there are few known results. Existing control methods for nonlinear DAEs have so far relied on deriving state space models for limited classes of problems. A new approach for state space modeling of DAEs is developed by formulating an equivalent nonlinear control problem. The zero dynamics of the control system represent the dynamics of the original DAE. This new connection between DAE model representation and nonlinear control is used to obtain state space representations for a general class of differential-algebraic systems. By relating nonlinear control concepts to DAE structural properties a sliding manifold is constructed that asymptotically satisfies the constraint equations. Sliding control techniques are combined with elements of singular perturbation theory to develop an efficient state space model with properties necessary for controller synthesis. This leads to the singularly perturbed sliding manifold (SPSM) approach for state space realization. The new approach is demonstrated by formulating a state space model of vapor compression cycles. This allows verification of the method and provides more insight into the problems associated with modeling differential algebraic systems.
by Brandon W. Gordon.
Ph.D.
Kunert, Gerd. "A note on the energy norm for a singularly perturbed model problem." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100062.
Повний текст джерелаMaddah, Sumayya Suzy. "Formal reduction of differential systems : Singularly-perturbed linear differential systems and completely integrable Pfaffian systems with normal crossings." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0065/document.
Повний текст джерелаIn this thesis, we are interested in the local analysis of singularly-perturbed linear differential systems and completely integrable Pfaffian systems in several variables. Such systems have a vast literature and arise profoundly in applications. However, their symbolic resolution is still open to investigation. Our approaches rely on the state of art of formal reduction of singular linear systems of ordinary differential equations (ODS) over univariate fields. In the case of singularly-perturbed linear differential systems, the complications arise mainly from the phenomenon of turning points. We extend notions introduced for the treatment of ODS to such systems and generalize corresponding algorithms to construct formal solutions in a neighborhood of a singularity. The underlying components of the formal reduction proposed are stand-alone algorithms as well and serve different purposes (e.g. rank reduction, classification of singularities, computing restraining index). In the case of Pfaffian systems, the complications arise from the interdependence of the multiple components which constitute the former and the multivariate nature of the field within which reduction occurs. However, we show that the formal invariants of such systems can be retrieved from an associated ODS, which limits computations to univariate fields. Furthermore, we complement our work with a rank reduction algorithm and discuss the obstacles encountered. The techniques developed herein paves the way for further generalizations of algorithms available for univariate differential systems to bivariate and multivariate ones, for different types of systems of functional equations
Kunert, Gerd. "Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes." Universitätsbibliothek Chemnitz, 2000. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200000867.
Повний текст джерелаKunert, Gerd. "Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100011.
Повний текст джерелаKunert, Gerd. "A posteriori H^1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100730.
Повний текст джерелаKunert, Gerd. "A posteriori error estimation for convection dominated problems on anisotropic meshes." Universitätsbibliothek Chemnitz, 2002. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200200255.
Повний текст джерелаKunert, Gerd. "A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes." Doctoral thesis, [S.l. : s.n.], 1999. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10324701.
Повний текст джерелаHulek, Charlotte. "Systèmes d'équations différentielles linéaires singulièrement perturbées et développements asymptotiques combinés." Phd thesis, Université de Strasbourg, 2014. http://tel.archives-ouvertes.fr/tel-01021178.
Повний текст джерелаMusolino, Paolo. "Singular perturbation and homogenization problems in a periodically perforated domain. A functional analytic approach." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3422452.
Повний текст джерелаQuesta Tesi è dedicata all'analisi di problemi di perturbazione singolare e omogeneizzazione nello spazio Euclideo periodicamente perforato. Studiamo il comportamento delle soluzioni di problemi al contorno per le equazioni di Laplace, di Poisson e di Helmholtz al tendere a 0 di parametri legati al diametro dei buchi o alla dimensione delle celle di periodicità. La Tesi è organizzata come segue. Nel Capitolo 1, presentiamo due costruzioni note di un analogo periodico della soluzione fondamentale dell'equazione di Laplace, e introduciamo potenziali di strato e di volume periodici per l'equazione di Laplace e alcuni risultati basilari di teoria del potenziale periodica. Il Capitolo 2 è dedicato a problemi di perturbazione singolare e omogeneizzazione per le equazioni di Laplace e Poisson con condizioni al bordo di Dirichlet e Neumann. Nel Capitolo 3 consideriamo il caso di problemi al contorno di Robin (lineari e nonlineari) per l'equazione di Laplace, mentre nel Capitolo 4 analizziamo problemi di trasmissione (lineari e nonlineari). Nel Capitolo 5 applichiamo i risultati del Capitolo 4 al fine di provare l'analiticità della conduttività effettiva di un composto periodico. Il Capitolo 6 è dedicato alla costruzione di un analogo periodico della soluzione fondamentale dell'equazione di Helmholtz e dei corrispondenti potenziali di strato. Nel Capitolo 7 raccogliamo alcuni risultati di teoria spettrale per l'operatore di Laplace in domini periodicamente perforati. Nel Capitolo 8 studiamo problemi di perturbazione singolare e di omogeneizzazione per l'equazione di Helmholtz con condizioni al contorno di Neumann. Nel Capitolo 9 consideriamo problemi di perturbazione singolare e di omogeneizzazione con condizioni al contorno di Dirichlet per l'equazione di Helmholtz, mentre nel Capitolo 10 studiamo problemi al contorno di Robin (lineari e nonlineari). Il Capitolo 11 è dedicato allo studio di potenziali di strato periodici per operatori differenziali generali del secondo ordine a coefficienti costanti. Alla fine della Tesi abbiamo incluso delle Appendici con alcuni risultati utilizzati.
Grosman, Sergey. "Adaptivity in anisotropic finite element calculations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600815.
Повний текст джерелаCaillerie, Nils. "Équations cinétiques stochastiques et déterministes dans le contexte des mathématiques appliquées à la biologie." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1117/document.
Повний текст джерелаIn this thesis, we study some biology inspired mathematical models. More precisely, we focus on kinetic partial differential equations. The fields of application of such equations are numerous but we focus here on propagation phenomena for invasive species, the Escherichia coli bacterium and the cane toad Rhinella marina, for example. The first part of this this does not establish any mathematical result. We build several models for the dispersion of the cane toad in Australia. We confront those very models to multiple statistical data (birth rate, survival rate, dispersal behaviors) to test their validity. Those models are based on velocity-jump processes and kinetic equations. In the second part, we study propagation phenomena on simpler kinetic models. We illustrate several methods to mathematically establish propagation speed in this models. This part leads us to establish convergence results of kinetic equations to Hamilton-Jacobi equations by the perturbed test function method. We also show how to use the Hamilton-Jacobi framework to establish spreading results et finally, we build travelling wave solutions for reaction-transport model. In the last part, we establish a stochastic diffusion limit result for a kinetic equation with a random term. To do so, we adapt the perturbed test function method on the formulation of a stochastic PDE in term of infinitesimal generators. The thesis also contains an annex which presents the data on toads’ trajectories used in the first part."
Shakti, D. "Numerics of singularly perturbed differential equations." Thesis, 2014. http://ethesis.nitrkl.ac.in/6258/1/E-99.pdf.
Повний текст джерелаYadav, Sangeeta. "Data Driven Stabilization Schemes for Singularly Perturbed Differential Equations." Thesis, 2023. https://etd.iisc.ac.in/handle/2005/6095.
Повний текст джерелаGoswami, Amartya. "Asymptotic analysis of singularly perturbed dynamical systems." Thesis, 2011. http://hdl.handle.net/10413/9760.
Повний текст джерелаThesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2011.
Li, Fang-wen, and 李芳雯. "Radial Basis Collocation Method for Singularly Perturbed Partial Differential Equations." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/06442167851802632152.
Повний текст джерела國立中山大學
應用數學系研究所
92
In this thesis, we integrate the particular solutions of singularly perturbed partial differential equations into radial basis collocation method to solve two kinds of boundary layer problem.
Govindarao, Lolugu. "Parameter Uniform Numerical Methods for Singularly Perturbed Parabolic Partial Differential Equations." Thesis, 2019. http://ethesis.nitrkl.ac.in/10169/1/2019_PhD_LGovindarao_515MA6012_Parameter.pdf.
Повний текст джерела"A higher-order energy expansion to two-dimensional singularly perturbed Neumann problems." 2004. http://library.cuhk.edu.hk/record=b5891877.
Повний текст джерелаThesis (M.Phil.)--Chinese University of Hong Kong, 2004.
Includes bibliographical references (leaves 51-55).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.5
Chapter 2 --- Some Preliminaries --- p.13
Chapter 3 --- "Approximate Function we,p" --- p.17
Chapter 4 --- "The Computation Of Je[we,p]" --- p.21
Chapter 5 --- The Signs of c1 And c3 --- p.30
Chapter 6 --- The Asymptotic Behavior of ue and Je[ue] --- p.35
Chapter 7 --- "The Proofs Of Theorem 1.1, Theorem 1.2 And Corol- lary 11" --- p.40
Appendix --- p.43
Bibliography --- p.51
Reibiger, Christian. "Optimal Control Problems with Singularly Perturbed Differential Equations as Side Constraints: Analysis and Numerics." Doctoral thesis, 2014. https://tud.qucosa.de/id/qucosa%3A28578.
Повний текст джерелаCOLUZZI, BARTOCCIONI BARBARA. "Theoretical models and numerical methods for the study of sub-cellular phenomena." Doctoral thesis, 2018. http://hdl.handle.net/11573/1186551.
Повний текст джерелаPark, Peter J. "Multiscale numerical methods for the singularly perturbed convection-diffusion equation." Thesis, 2000. https://thesis.library.caltech.edu/783/1/Park_pj_2000.pdf.
Повний текст джерелаLamač, Jan. "Adaptivní metody pro singulárně porušené parciální diferenciální rovnice." Doctoral thesis, 2017. http://www.nusl.cz/ntk/nusl-368918.
Повний текст джерела