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Academic literature on the topic 'Linear ODE'

Author: Grafiati

Published: 1 April 2023

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Journal articles on the topic "Linear ODE"

1

Deutscher, Joachim, Nicole Gehring, and Richard Kern. "Output feedback control of general linear heterodirectional hyperbolic ODE–PDE–ODE systems." Automatica 95 (September 2018): 472–80. http://dx.doi.org/10.1016/j.automatica.2018.06.021.

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Radnef, Sorin. "Analytic Solution of Non-Autonomous Linear ODE." PAMM 6, no. 1 (2006): 651–52. http://dx.doi.org/10.1002/pamm.200610306.

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Hu, Jie, Huihui Qin, and Xiaodan Fan. "Can ODE gene regulatory models neglect time lag or measurement scaling?" Bioinformatics 36, no. 13 (2020): 4058–64. http://dx.doi.org/10.1093/bioinformatics/btaa268.

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Abstract Motivation Many ordinary differential equation (ODE) models have been introduced to replace linear regression models for inferring gene regulatory relationships from time-course gene expression data. But, since the observed data are usually not direct measurements of the gene products or there is an unknown time lag in gene regulation, it is problematic to directly apply traditional ODE models or linear regression models. Results We introduce a lagged ODE model to infer lagged gene regulatory relationships from time-course measurements, which are modeled as linear transformation of the gene products. A time-course microarray dataset from a yeast cell-cycle study is used for simulation assessment of the methods and real data analysis. The results show that our method, by considering both time lag and measurement scaling, performs much better than other linear and ODE models. It indicates the necessity of explicitly modeling the time lag and measurement scaling in ODE gene regulatory models. Availability and implementation R code is available at https://www.sta.cuhk.edu.hk/xfan/share/lagODE.zip.

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Lorber, Alfred A., Graham F. Carey, and Wayne D. Joubert. "ODE Recursions and Iterative Solvers for Linear Equations." SIAM Journal on Scientific Computing 17, no. 1 (1996): 65–77. http://dx.doi.org/10.1137/0917006.

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Shi-Da, Liu, Fu Zun-Tao, Liu Shi-Kuo, Xin Guo-Jun, Liang Fu-Ming, and Feng Bei-Ye. "Solitary Wave in Linear ODE with Variable Coefficients." Communications in Theoretical Physics 39, no. 6 (2003): 643–46. http://dx.doi.org/10.1088/0253-6102/39/6/643.

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Ayadi, Habib. "Exponential stabilization of an ODE–linear KdV cascaded system with boundary input delay." IMA Journal of Mathematical Control and Information 37, no. 4 (2020): 1506–23. http://dx.doi.org/10.1093/imamci/dnaa022.

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Abstract This paper considers the well posedness and the exponential stabilization problems of a cascaded ordinary differential equation (ODE)–partial differential equation (PDE) system. The considered system is governed by a linear ODE and the one-dimensional linear Korteweg–de Vries (KdV) equation posed on a bounded interval. For the whole system, a control input delay acts on the left boundary of the KdV domain by Dirichlet condition. Whereas, the KdV acts back on the ODE by Dirichlet interconnection on the right boundary. Firstly, we reformulate the system in question as an undelayed ODE-coupled KdV-transport system. Secondly, we use the so-called infinite dimensional backstepping method to derive an explicit feedback control law that transforms system under consideration to a well-posed and exponentially stable target system. Finally, by invertibility of such design, we use semigroup theory and Lyapunov analysis to prove the well posedness and the exponential stabilization in a suitable functional space of the original plant, respectively.

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Imoni, Sunday Obomeviekome, D. I. Lanlege, E. M. Atteh, and J. O. Ogbondeminu. "FORMULATION OF BLOCK SCHEMES WITH LINEAR MULTISTEP METHOD FOR THE APPROXIMATION OF FIRST-ORDER IVPS." FUDMA JOURNAL OF SCIENCES 4, no. 3 (2020): 313–22. http://dx.doi.org/10.33003/fjs-2020-0403-260.

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ABSTRACT In this paper, formulation of an efficient numerical schemes for the approximation first-order initial value problems (IVPs) of ordinary differential equations (ODE) is presented. The method is a block scheme for some k-step linear multi-step methods (and) using the Hermite Polynomials a basis function. The continuous and discrete linear multi-step methods (LMM) are formulated through the technique of collocation and interpolation. Numerical examples of ODE have been examined and results obtained show that the proposed scheme can be efficient in solving initial value problems of first order ODE.

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POSPÍŠIL, JIŘÍ, ZDENĚK KOLKA, JANA HORSKÁ, and JAROMÍR BRZOBOHATÝ. "SIMPLEST ODE EQUIVALENTS OF CHUA'S EQUATIONS." International Journal of Bifurcation and Chaos 10, no. 01 (2000): 1–23. http://dx.doi.org/10.1142/s0218127400000025.

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The so-called elementary canonical state models of the third-order piecewise-linear (PWL) dynamical systems, as the simplest ODE equivalents of Chua's equations, are presented. Their mutual relations using the linear topological conjugacy are demonstrated in order to show in detail that Chua's equations and their canonical ODE equivalents represent various forms of qualitatively equivalent models of third-order dynamical systems. New geometrical aspects of the corresponding transformations together with examples of typical chaotic attractors in the stereoscopic view, give the possibility of a deeper insight into the third-order system dynamics.

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Mukhopadhyay, S., R. Picard, S. Trostorff, and M. Waurick. "A note on a two-temperature model in linear thermoelasticity." Mathematics and Mechanics of Solids 22, no. 5 (2015): 905–18. http://dx.doi.org/10.1177/1081286515611947.

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We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration. With the abstract perspective of evolutionary equations, the two-temperature model turns out to be a coupled system of the elastic equations and an abstract ordinary differential equation (ODE). Following this line of reasoning, we propose another model which is entirely an abstract ODE. We also highlight an alternative method for a two-temperature model, which might be of independent interest.

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Aksan, Emine. "An application of cubic B-Spline finite element method for the Burgers` equation." Thermal Science 22, Suppl. 1 (2018): 195–202. http://dx.doi.org/10.2298/tsci170613286a.

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It is difficult to achieve exact solution of non-linear PDE, directly. Sometimes, it is possible to convert non-linear PDE into equivalent linear PDE by applying a convenient transformation. Hence, Burgers? equation replaces with heat equation by means of the Hope-Cole transformation. In this study, Burgers? equation was converted to a set of non-linear ODE by keeping non-linear structure of Burgers? equation. In this case, solutions for each of the non-linear ODE were obtained by the help of the cubic B-spline finite element method. Model problems were considered to verify the efficiency of this method. Agreement of the solutions was shown with graphics and tables.

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Dissertations / Theses on the topic "Linear ODE"

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D'Augustine, Anthony Frank. "MATLODE: A MATLAB ODE Solver and Sensitivity Analysis Toolbox." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/83081.

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Sensitivity analysis quantifies the effect that of perturbations of the model inputs have on the model's outputs. Some of the key insights gained using sensitivity analysis are to understand the robustness of the model with respect to perturbations, and to select the most important parameters for the model. MATLODE is a tool for sensitivity analysis of models described by ordinary differential equations (ODEs). MATLODE implements two distinct approaches for sensitivity analysis: direct (via the tangent linear model) and adjoint. Within each approach, four families of numerical methods are implemented, namely explicit Runge-Kutta, implicit Runge-Kutta, Rosenbrock, and single diagonally implicit Runge-Kutta. Each approach and family has its own strengths and weaknesses when applied to real world problems. MATLODE has a multitude of options that allows users to find the best approach for a wide range of initial value problems. In spite of the great importance of sensitivity analysis for models governed by differential equations, until this work there was no MATLAB ordinary differential equation sensitivity analysis toolbox publicly available. The two most popular sensitivity analysis packages, CVODES [8] and FATODE [10], are geared toward the high performance modeling space; however, no native MATLAB toolbox was available. MATLODE fills this need and offers sensitivity analysis capabilities in MATLAB, one of the most popular programming languages within scientific communities such as chemistry, biology, ecology, and oceanogra- phy. We expect that MATLODE will prove to be a useful tool for these communities to help facilitate their research and fill the gap between theory and practice.<br>Master of Science

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Albishi, Njwd. "Three-and four-derivative Hermite-Birkhoff-Obrechkoff solvers for stiff ODE." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34332.

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Three- and four-derivative k-step Hermite-Birkhoff-Obrechkoff (HBO) methods are constructed for solving stiff systems of first-order differential equations of the form y'= f(t,y), y(t0) = y0. These methods use higher derivatives of the solution y as in Obrechkoff methods. We compute their regions of absolute stability and show the three- and four-derivative HBO are A( 𝜶)-stable with 𝜶 > 71 ° and 𝜶 > 78 ° respectively. We conduct numerical tests and show that our new methods are more efficient than several existing well-known methods.

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DELLA, MARCA ROSSELLA. "Problemi di controllo in epidemiologia matematica e comportamentale." Doctoral thesis, Università degli studi di Modena e Reggio Emilia, 2021. http://hdl.handle.net/11380/1237622.

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Nonostante i progressi nell'eliminazione di infezioni da lungo in circolazione, gli ultimi decenni hanno visto la continua comparsa o ricomparsa di malattie infettive. Esse non solo minacciano la salute globale, ma i costi generati da epidemie nell’uomo e negli animali sono responsabili di significative perdite economiche. I modelli matematici della diffusione di malattie infettive hanno svolto un ruolo significativo nel controllo delle infezioni. Da un lato, hanno dato un importante contributo alla comprensione epidemiologica degli andamenti di scoppi epidemici; d'altro canto, hanno concorso a determinare come e quando applicare le misure di controllo al fine di contenere rapidamente ed efficacemente le epidemie. Ciononostante, per dare forma alle politiche di sanità pubblica, è essenziale acquisire una migliore e più completa comprensione delle azioni efficaci per controllare le infezioni, impiegando nuovi livelli di complessità. Questo è stato l'obiettivo fondamentale della ricerca che ho svolto durante il dottorato; in questa tesi i prodotti di questa ricerca sono raccolti e interconnessi. Tuttavia, poiché fuori contesto, altri problemi a cui mi sono interessata sono stati esclusi: essi riguardano le malattie autoimmuni e l'ecologia del paesaggio. Si inizia con un capitolo introduttivo, che ripercorre la storia dei modelli epidemici, le motivazioni e gli incredibili progressi. Sono due gli aspetti su cui ci concentriamo: i) la valutazione qualitativa e quantitativa di strategie di controllo specifiche per il problema in questione (attraverso, ad esempio, il controllo ottimo o le politiche a soglia); ii) l'incorporazione nel modello dei cambiamenti nel comportamento umano in risposta alla dinamica della malattia. In questo quadro si inseriscono e contestualizzano i nostri studi. Di seguito, a ciascuno di essi è dedicato un capitolo specifico. Le tecniche utilizzate includono la costruzione di modelli appropriati dati da equazioni differenziali ordinarie non lineari, la loro analisi qualitativa (tramite, ad esempio, la teoria della stabilità e delle biforcazioni), la parametrizzazione e la validazione con i dati disponibili. I test numerici sono eseguiti con avanzati metodi di simulazione di sistemi dinamici. Per i problemi di controllo ottimo, la formulazione segue l'approccio classico di Pontryagin, mentre la risoluzione numerica è svolta da metodi di ottimizzazione sia diretta che indiretta. Nel capitolo 1, utilizzando come base di partenza un modello Suscettibili-Infetti-Rimossi, affrontiamo il problema di minimizzare al contempo la portata e il tempo di eradicazione di un’epidemia tramite strategie di vaccinazione o isolamento ottimali. Un modello epidemico tra due sottopopolazioni, che descrive la dinamica di Suscettibili e Infetti in malattie della fauna selvatica, è formulato e analizzato nel capitolo 2. Qui, vengono confrontati due tipi di strategie di abbattimento localizzato: proattivo e reattivo. Il capitolo 3 tratta di un modello per la trasmissione di malattie pediatriche prevenibili con vaccino, dove la vaccinazione dei neonati segue la dinamica del gioco dell’imitazione ed è affetta da campagne di sensibilizzazione da parte del sistema sanitario. La vaccinazione è anche incorporata nel modello del capitolo 4. Qui, essa è rivolta a individui suscettibili di ogni età ed è funzione dell’informazione e delle voci circolanti sulla malattia. Inoltre, si assume che l'efficacia del vaccino sia parziale ed evanescente col passare del tempo. L'ultimo capitolo è dedicato alla tuttora in corso pandemia di COVID-19. Si costruisce un modello epidemico con tassi di contatto e di quarantena dipendenti dall’informazione circolante. Il modello è applicato al caso italiano e incorpora le progressive restrizioni durante il lockdown.<br>Despite major achievements in eliminating long-established infections (as in the very well known case of smallpox), recent decades have seen the continual emergence or re-emergence of infectious diseases (last but not least COVID-19). They are not only threats to global health, but direct and indirect costs generated by human and animal epidemics are responsible for significant economic losses worldwide. Mathematical models of infectious diseases spreading have played a significant role in infection control. On the one hand, they have given an important contribution to the biological and epidemiological understanding of disease outbreak patterns; on the other hand, they have helped to determine how and when to apply control measures in order to quickly and most effectively contain epidemics. Nonetheless, in order to shape local and global public health policies, it is essential to gain a better and more comprehensive understanding of effective actions to control diseases, by finding ways to employ new complexity layers. This was the main focus of the research I have carried out during my PhD; the products of this research are collected and connected in this thesis. However, because out of context, other problems I interested in have been excluded from this collection: they rely in the fields of autoimmune diseases and landscape ecology. We start with an Introduction chapter, which traces the history of epidemiological models, the rationales and the breathtaking incremental advances. We focus on two critical aspects: i) the qualitative and quantitative assessment of control strategies specific to the problem at hand (via e.g. optimal control or threshold policies); ii) the incorporation into the model of the human behavioral changes in response to disease dynamics. In this framework, our studies are inserted and contextualized. Hereafter, to each of them a specific chapter is devoted. The techniques used include the construction of appropriate models given by non-linear ordinary differential equations, their qualitative analysis (via e.g. stability and bifurcation theory), the parameterization and validation with available data. Numerical tests are performed with advanced simulation methods of dynamical systems. As far as optimal control problems are concerned, the formulation follows the classical approach by Pontryagin, while both direct and indirect optimization methods are adopted for the numerical resolution. In Chapter 1, within a basic Susceptible-Infected-Removed model framework, we address the problem of minimizing simultaneously the epidemic size and the eradication time via optimal vaccination or isolation strategies. A two-patches metapopulation epidemic model, describing the dynamics of Susceptibles and Infected in wildlife diseases, is formulated and analyzed in Chapter 2. Here, two types of localized culling strategies are considered and compared: proactive and reactive. Chapter 3 concerns a model for vaccine-preventable childhood diseases transmission, where newborns vaccination follows an imitation game dynamics and is affected by awareness campaigns by the public health system. Vaccination is also incorporated in the model of Chapter 4. Here, it addresses susceptible individuals of any age and depends on the information and rumors about the disease. Further, the vaccine effectiveness is assumed to be partial and waning over time. The last Chapter 5 is devoted to the ongoing pandemic of COVID-19. We build an epidemic model with information-dependent contact and quarantine rates. The model is applied to the Italian case and explicitly incorporates the progressive lockdown restrictions.

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Hewitt, Laura L. "General linear methods for the solution of ODEs." Thesis, University of Bath, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.516948.

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Farris, Thomas Edward. "Searching for the CP-odd Higgs at a linear collider /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2003. http://uclibs.org/PID/11984.

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Fernandes, Ray Stephen. "Very singular solutions of odd-order PDEs, with linear and nonlinear dispersion." Thesis, University of Bath, 2008. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.507233.

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Asymptotic properties of solutions of the linear dispersion equation ut = uxxx in R × R+, and its (2k + 1)th-order generalisations are studied. General Hermitian spectral theory and asymptotic behaviour of its kernel, for the rescaled operator B = D3 + 1 3 yDy + 1 3 I, is developed, where a complete set of bi-orthonormal pair of eigenfunctions, {ψβ}, {ψ∗β }, are found. The results apply to the construction of VSS (very singular solutions) of the semilinear equation with absorption ut = uxxx − |u|p−1u in R × R+, where p > 1, which serves as a basic model for various applications, including the classic KdV area. Finally, the nonlinear dispersion equations such as ut = (|u|nu)xxx in R × R+, and ut = (|u|nu)xxx − |u|p−1u in R × R+, where n > 0, are studied and their “nonlinear eigenfunctions” are constructed. The basic tools include numerical methods and “homotopy-deformation” approaches, where the limits n → 0 and n → +∞ turn out to be fruitful. Local existence and uniqueness is proved and some bounds on the highly oscillatory tail are found. These odd-order models were not treated in existing mathematical literature, from the proposed point of view.

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Paditz, Ludwig. "Using ClassPad-technology in the education of students of electrical engineering (Fourier- and Laplace-Transformation)." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80814.

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By the help of several examples the interactive work with the ClassPad330 is considered. The student can solve difficult exercises of practical applications step by step using the symbolic calculation and the graphic possibilities of the calculator. Sometimes several fields of mathematics are combined to solve a problem. Let us consider the ClassPad330 (with the actual operating system OS 03.03) and discuss on some new exercises in analysis, e.g. solving a linear differential equation by the help of the Laplace transformation and using the inverse Laplace transformation or considering the Fourier transformation in discrete time (the Fast Fourier Transformation FFT and the inverse FFT). We use the FFT- and IFFT-function to study periodic signals, if we only have a sequence generated by sampling the time signal. We know several ways to get a solution. The techniques for studying practical applications fall into the following three categories: analytic, graphic and numeric. We can use the Classpad software in the handheld or in the PC (ClassPad emulator version of the handheld).

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Paditz, Ludwig. "Using ClassPad-technology in the education of students of electricalengineering (Fourier- and Laplace-Transformation)." Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 469 - 474, 2012. https://slub.qucosa.de/id/qucosa%3A1799.

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By the help of several examples the interactive work with the ClassPad330 is considered. The student can solve difficult exercises of practical applications step by step using the symbolic calculation and the graphic possibilities of the calculator. Sometimes several fields of mathematics are combined to solve a problem. Let us consider the ClassPad330 (with the actual operating system OS 03.03) and discuss on some new exercises in analysis, e.g. solving a linear differential equation by the help of the Laplace transformation and using the inverse Laplace transformation or considering the Fourier transformation in discrete time (the Fast Fourier Transformation FFT and the inverse FFT). We use the FFT- and IFFT-function to study periodic signals, if we only have a sequence generated by sampling the time signal. We know several ways to get a solution. The techniques for studying practical applications fall into the following three categories: analytic, graphic and numeric. We can use the Classpad software in the handheld or in the PC (ClassPad emulator version of the handheld).

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Starkloff, Hans-Jörg, and Ralf Wunderlich. "Stationary solutions of linear ODEs with a randomly perturbed system matrix and additive noise." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501335.

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The paper considers systems of linear first-order ODEs with a randomly perturbed system matrix and stationary additive noise. For the description of the long-term behavior of such systems it is necessary to study their stationary solutions. We deal with conditions for the existence of stationary solutions as well as with their representations and the computation of their moment functions. Assuming small perturbations of the system matrix we apply perturbation techniques to find series representations of the stationary solutions and give asymptotic expansions for their first- and second-order moment functions. We illustrate the findings with a numerical example of a scalar ODE, for which the moment functions of the stationary solution still can be computed explicitly. This allows the assessment of the goodness of the approximations found from the derived asymptotic expansions.

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Barreau, Matthieu. "Stability analysis of coupled ordinary differential systems with a string equation : application to a drilling mechanism." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30058.

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Cette thèse porte sur l'analyse de stabilité de couplage entre deux systèmes, l'un de dimension finie et l'autre infinie. Ce type de systèmes apparait en physique car il est intimement lié aux modèles de structures. L'analyse générique de tels systèmes est complexe à cause des natures très différentes de chacun des sous-systèmes. Ici, l'analyse est conduite en utilisant deux méthodologies. Tout d'abord, la séparation quadratique est utilisée pour traiter le côté fréquentiel de ce système couplé. L'autre méthode est basée sur la théorie de Lyapunov pour prouver la stabilité asymptotique de l'interconnexion. Tous ces résultats sont obtenus en utilisant la méthode de projection de l'état de dimension infinie sur une base polynomiale. Il est alors possible de prendre en compte le couplage entre les deux systèmes et ainsi d'obtenir des tests numériques fiables, rapides et peu conservatifs. De plus, une hiérarchie de conditions est établie dans le cas de Lyapunov. L'application au cas concret du forage pétrolier est proposée pour illustrer l'efficacité de la méthode et les nouvelles perspectives qu'elle offre. Par exemple, en utilisant la notion de stabilité pratique, nous avons montré qu'une tige de forage controlée à l'aide d'un PI est sujette à un cycle limite et qu'il est possible d'estimer son amplitude<br>This thesis is about the stability analysis of a coupled finite dimensional system and an infinite dimensional one. This kind of systems emerges in the physics since it is related to the modeling of structures for instance. The generic analysis of such systems is complex, mainly because of their different nature. Here, the analysis is conducted using different methodologies. First, the recent Quadratic Separation framework is used to deal with the frequency aspect of such systems. Then, a second result is derived using a Lyapunov-based argument. All the results are obtained considering the projections of the infinite dimensional state on a basis of polynomials. It is then possible to take into account the coupling between the two systems. That results in tractable and reliable numerical tests with a moderate conservatism. Moreover, a hierarchy on the stability conditions is shown in the Lyapunov case. The real application to a drilling mechanism is proposed to illustrate the efficiency of the method and it opens new perspectives. For instance, using the notion of practical stability, we show that a PI-controlled drillstring is subject to a limit cycle and that it is possible to estimate its amplitude

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Books on the topic "Linear ODE"

1

Saylor, Paul E. Linear iterative solvers for implicit ode methods. National Aeronautics and Space Administration, Langley Research Center, 1990.

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C, Sprott Julien, and ebrary Inc, eds. 2-D quadratic maps and 3-D ODE systems: A rigorous approach. World Scientific Pub. Co., 2010.

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Robert, Hermann. Lie-theoretic ODE numerical analysis, mechanics, and differential systems. Math Sci Press, 1994.

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Der Diskos von Phaistos: Fremdeinfluss oder kretisches Erbe? Books on Demand, 2005.

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Manichev, Vladimir, Valentina Glazkova, and Кузьмина Анастасия. Numerical methods. The authentic and exact solution of the differential and algebraic equations in SAE systems of SAPR. INFRA-M Academic Publishing LLC., 2016. http://dx.doi.org/10.12737/13138.

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In the manual classical numerical methods are considered and algorithms for the decision of systems of the ordinary differential equations (ODE), nonlinear and linear algebraic equations (NAU and LAU), and also ways of ensuring reliability and demanded accuracy of results of the decision. Ideas, which still not are stated are reflected in textbooks on calculus mathematics, namely: decision systems the ODE without reduction to a normal form of Cauchy resolved rather derivative, and refusal from any numerical an equivalent - nykh of transformations of the initial equations of mathematical models and is- the hodnykh of data because such transformations can change properties of models at a variation of coefficients in corresponding urav- neniyakh. It is intended for students, graduate students and teachers of higher education institutions in the direction of preparation &#34;Informatics and computer facilities&#34;. The grant will also be useful for engineers and scientists on the corresponding specialties.

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Hung, Pei-Ken. The linear stability of the Schwarzschild spacetime in the harmonic gauge: Odd part. [publisher not identified], 2018.

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Hettlich, Frank. Vorkurs Mathematik: Ein Arbeitsheft zur Vorbereitung auf den Start eines Hochschulstudiums in Mathematik, Informatik einer Naturwissenschaft oder einer Ingenieurwissenschaft. Shaker, 2004.

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Zemanian, A. H. Realizability theory for continuous linear systems. Dover, 1995.

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The minimal polynomials of unipotent elements in irreducible representations of the classical groups in odd characteristic. American Mathematical Society, 2009.

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Andreischeva, Elena. A collection of practical and laboratory works in higher mathematics. Elements of linear and vector algebra. Workshop. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1089868.

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This textbook can be considered as a basic manual to address both typical and General character of the duties of one of the sections of the course higher mathematics — "Linear and vector algebra". The purpose of the textbook is to help the cadets of the training and methodological assistance in preparing for practical classes and during these classes to help to develop their independence, initiative and creativity in solving problems, acquire the necessary practical skills. Meets the requirements of Federal state educational standards of higher education of the last generation. For students of higher educational institutions studying the mathematical disciplines.

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Book chapters on the topic "Linear ODE"

1

Enns, Richard H., and George C. McGuire. "Linear ODE Models." In Computer Algebra Recipes. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0171-4_7.

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Balser, Werner. "Formal solutions to non-linear ODE." In From Divergent Power Series to Analytic Functions. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073572.

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Redaud, Jeanne, Federico Bribiesca-Argomedo, and Jean Auriol. "Practical Output Regulation and Tracking for Linear ODE-hyperbolic PDE-ODE Systems." In Advances in Distributed Parameter Systems. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-94766-8_7.

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Tadie. "Oscillation Criteria for some Semi-Linear Emden–Fowler ODE." In Integral Methods in Science and Engineering. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16727-5_51.

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Gray, Alfred, Michael Mezzino, and Mark A. Pinsky. "Using ODE to Solve Second-Order Linear Differential Equations." In Introduction to Ordinary Differential Equations with Mathematica®. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-2242-2_10.

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Tang, Ying, Christophe Prieur, and Antoine Girard. "Singular Perturbation Approach for Linear Coupled ODE-PDE Systems." In Delays and Interconnections: Methodology, Algorithms and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11554-8_1.

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Dey, Anindya. "Second Order Linear Ode: Solution Techniques & Qualitative Analysis." In Differential Equations. CRC Press, 2021. http://dx.doi.org/10.1201/9781003205982-6.

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Botchev, Mike A. "Time-Exact Solution of Large Linear ODE Systems by Block Krylov Subspace Projections." In Mathematics in Industry. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05365-3_55.

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Coster, C., and P. Habets. "Upper and Lower Solutions in the Theory of Ode Boundary Value Problems: Classical and Recent Results." In Non Linear Analysis and Boundary Value Problems for Ordinary Differential Equations. Springer Vienna, 1996. http://dx.doi.org/10.1007/978-3-7091-2680-6_1.

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Ryzhikov, Ivan, Eugene Semenkin, and Shakhnaz Akhmedova. "Linear ODE Coefficients and Initial Condition Estimation with Co-operation of Biology Related Algorithms." In Lecture Notes in Computer Science. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41000-5_23.

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Conference papers on the topic "Linear ODE"

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Huo, Guanying, Xin Jiang, Danlei Ye, et al. "Linear ODE Based Geometric Modelling for Compressor Blades." In 2017 2nd International Conference on Electrical, Automation and Mechanical Engineering (EAME 2017). Atlantis Press, 2017. http://dx.doi.org/10.2991/eame-17.2017.53.

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Saba, David Bou, Federico Bribiesca-Argomedo, Michael Di Loreto, and Damien Eberard. "Strictly Proper Control Design for the Stabilization of 2×2 Linear Hyperbolic ODE-PDE-ODE Systems." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9030248.

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Melezhik, A. "Polynomial solutions of the third-order Fuchsian linear ODE." In International Seminar Day on Diffraction Millennium Workshop. Proceedings. IEEE, 2000. http://dx.doi.org/10.1109/dd.2000.902361.

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Najafi, Mahmoud, M. Ramezanizadeh, Donald Fincher, and H. Massah. "Analysis of a non-linear parabolic ODE via decomposition." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4913001.

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Khatibi, Seyedhamidreza, Guilherme Ozorio Cassol, and Stevan Dubljevic. "Linear model predictive control for a cascade ODE-PDE system." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147269.

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Cristofaro, Andrea, and Francesco Ferrante. "Unknown Input Observer design for coupled PDE/ODE linear systems." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9304374.

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Venkataraman, P. "Solving Inverse ODE Using Bezier Functions." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86331.

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The simplest inverse boundary value problem is to identify the differential equation and the boundary conditions from a given set of discrete data points. For an ordinary differential equation, it would involve finding a function, which when expressed through some function of itself and its derivatives, and integrated using particular boundary conditions would generate the given data. Parametric Bezier functions are excellent candidates for these functions. They allow efficient approximation of data and its derivative content. The Bezier function is smooth and continuous to a high degree. In this paper the best Bezier function to fit the data represents this function which is being sought. This Bezier approximation also determines the boundary conditions. Next, a generic form of the differential equation is assumed. The Bezier function and its derivatives are then used in this generic form to establish the exponents and coefficients of the various terms in the actual differential equation. The paper looks at homogeneous ordinary differential equations and shows it can recover the exact form of both linear and nonlinear differential equations. Two examples are presented. The first example uses data from the Bessel equation, representing a linear equation. The second example uses the data from the Blassius equation which is nonlinear. In both cases the exact form of the equation is identified from the given discrete data.

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Chaparova, Julia V., Eli P. Kalcheva, and Miglena N. Koleva. "Numerical investigation of multiple periodic solutions of fourth-order semi-linear ODE." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766780.

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Serban, Radu, and Alan C. Hindmarsh. "CVODES: The Sensitivity-Enabled ODE Solver in SUNDIALS." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85597.

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CVODES, which is part of the SUNDIALS software suite, is a stiff and nonstiff ordinary differential equation initial value problem solver with sensitivity analysis capabilities. CVODES is written in a data-independent manner, with a highly modular structure to allow incorporation of different preconditioning and/or linear solver methods. It shares with the other SUNDIALS solvers several common modules, most notably the generic kernel of vector operations and a set of generic linear solvers and preconditioners. CVODES solves the IVP by one of two methods — backward differentiation formula or Adams-Moulton — both implemented in a variable-step, variable-order form. The forward sensitivity module in CVODES implements the simultaneous corrector method, as well as two flavors of staggered corrector methods. Its adjoint sensitivity module provides a combination of checkpointing and cubic Hermite interpolation for the efficient generation of the forward solution during the adjoint system integration. We describe the current capabilities of CVODES, its design principles, and its user interface, and provide an example problem to illustrate the performance of CVODES.

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Auzinger, Winfried, Petro Pukach, Roksolyana Stolyarchuk, and Myroslava Vovk. "Adaptive Numerics for Linear ODE Systems with Time-Dependent Data; Application in Photovoltaics." In 2020 IEEE XVIth International Conference on the Perspective Technologies and Methods in MEMS Design (MEMSTECH). IEEE, 2020. http://dx.doi.org/10.1109/memstech49584.2020.9109442.

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Reports on the topic "Linear ODE"

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Vigil, M. G., and D. L. Marchi. Annular precision linear shaped charge flight termination system for the ODES program. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/10165513.

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Gardner C. J. Envelope Parameters for Linear Coupled Motion in Terms of the One-Turn Transfer Matrix. Office of Scientific and Technical Information (OSTI), 1996. http://dx.doi.org/10.2172/1151345.

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Mathias, Lon J., and Ralph M. Bozen. Linear and Star-Branched Siloxy-Silane Polymers: One Pot A-B Polymerization and End-Capping. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada252195.

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Tygert, Mark. Fast Algorithms for the Solution of Eigenfunction Problems for One-Dimensional Self-Adjoint Linear Differential Operators. Defense Technical Information Center, 2005. http://dx.doi.org/10.21236/ada458901.

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Baader, Franz, Anees ul Mehdi, and Hongkai Liu. Integrate Action Formalisms into Linear Temporal Description Logics. Technische Universität Dresden, 2009. http://dx.doi.org/10.25368/2022.172.

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The verification problem for action logic programs with non-terminating behaviour is in general undecidable. In this paper, we consider a restricted setting in which the problem becomes decidable. On the one hand, we abstract from the actual execution sequences of a non-terminating program by considering infinite sequences of actions defined by a Büchi automaton. On the other hand, we assume that the logic underlying our action formalism is a decidable description logic rather than full first-order predicate logic.

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Hong Qin and Ronald C. Davidson. Self-Similar Nonlinear Dynamical Solutions for One-Component Nonneutral Plasma in a Time-Dependent Linear Focusing Field. Office of Scientific and Technical Information (OSTI), 2011. http://dx.doi.org/10.2172/1029998.

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ZOTOVA, V. A., E. G. SKACHKOVA, and T. D. FEOFANOVA. METHODOLOGICAL FEATURES OF APPLICATION OF SIMILARITY THEORY IN THE CALCULATION OF NON-STATIONARY ONE-DIMENSIONAL LINEAR THERMAL CONDUCTIVITY OF A ROD. Science and Innovation Center Publishing House, 2022. http://dx.doi.org/10.12731/2227-930x-2022-12-1-2-43-53.

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The article describes the methodological features of the analytical solution of the problem of non-stationary one-dimensional linear thermal conductivity of the rod. The authors propose to obtain a solution to such problems by the method of finite differences using the Fourier similarity criterion. This approach is especially attractive because the similarity theory in the vast majority of cases makes it possible to do without expensive experiments and obtain simple solutions for a wide range of problems.

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R.P. Ewing and D.W. Meek. One Line or Two? Perspectives on Piecewise Regression. Office of Scientific and Technical Information (OSTI), 2006. http://dx.doi.org/10.2172/899336.

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Hanson, Hans, and Nicholas C. Kraus. T-Head Groin Advancements in One-Line Modeling (Genesis/T). Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada612482.

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O'Connell, R. F. Quantum Transport, Noise and Non-Linear Dissipative Effects in One- and Two-Dimensional Systems and Associated Sub-Micron and Nanostructure Devices. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada250895.

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