Relevant bibliographies by topics / Linear singularly perturbed problem

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Linear singularly perturbed problem'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Linear singularly perturbed problem"

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Dauylbayev, Muratkhan, Marat Akhmet, and Aviltay Nauryzbay. "ASYMPTOTIC EXPANSION OF THE SOLUTION FOR SINGULARPERTURBED LINEAR IMPULSIVE SYSTEMS." Journal of Mathematics, Mechanics and Computer Science 122, no. 2 (2024): 14–26. http://dx.doi.org/10.26577/jmmcs2024-122-02-b2.

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In this study, a singularly perturbed linear impulsive system with singularly perturbed impulses is considered. Many books discuss different types of singular perturbation problems. In the present work, an impulse system is considered in which a small parameter is introduced into the impulse equation. This is the main novelty of our study, since other works [25] have only considered a small parameter in the differential equation. A necessary condition is also established to prevent the impulse function from bloating as the parameter approaches zero. As a result, the notion of singularity for d
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Sharip, B., and А. Т. Yessimova. "ESTIMATION OF A BOUNDARY VALUE PROBLEM SOLUTION WITH INITIAL JUMP FOR LINEAR DIFFERENTIAL EQUATION." BULLETIN Series of Physics & Mathematical Sciences 69, no. 1 (2020): 168–73. http://dx.doi.org/10.51889/2020-1.1728-7901.28.

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The paper considers a boundary value problem for a singularly perturbed linear differential equation with constant third-order coefficients. In this problem, a small parameter is indicated before the highest derivatives that are part of the differential equation and the boundary condition at t = 0.The fundamental system of solutions of a homogeneous singularly perturbed differential equation is constructed on the basis of asymptotic representations obtained for the roots of the corresponding characteristic equation. This system was used to construct the Cauchy function, special functions of bo
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PERJAN, ANDREI, and GALINA RUSU. "Abstract linear second order differential equations with two small parameters and depending on time operators." Carpathian Journal of Mathematics 33, no. 2 (2017): 233–46. http://dx.doi.org/10.37193/cjm.2017.02.10.

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In a real Hilbert space H consider the following singularly perturbed Cauchy problem. We study the behavior of solutions uεδ to this problem in two different cases: ε → 0 and δ ≥ δ0 > 0; ε → 0 and δ → 0, relative to solution to the corresponding unperturbed problem. We obtain some a priori estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the perturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of t = 0. We show the boun
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Zhumanazarova, Assiya, and Young Im Cho. "Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem." Mathematics 8, no. 2 (2020): 213. http://dx.doi.org/10.3390/math8020213.

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In this study, the asymptotic behavior of the solutions to a boundary value problem for a third-order linear integro-differential equation with a small parameter at the two higher derivatives has been examined, under the condition that the roots of the additional characteristic equation are negative. Via the scheme of methods and algorithms pertaining to the qualitative study of singularly perturbed problems with initial jumps, a fundamental system of solutions, the Cauchy function, and the boundary functions of a homogeneous singularly perturbed differential equation are constructed. Analytic
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Mirzakulova, A. E., and K. T. Konisbayeva. "Uniform asymptotic expansion of the solution for the initial value problem with a piecewise constant argument." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 116, no. 4 (2024): 138–48. https://doi.org/10.31489/2024m4/138-148.

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The article is devoted to the study of a singularly perturbed initial problem for a linear differential equation with a piecewise constant argument second-order for a small parameter. This paper is considered the asymptotic expansion of the solution to the Cauchy problem for singularly perturbed differential equations with piecewise-constant argument. The initial value problem for first order linear differential equations with piecewise-constant argument was obtained that determined the regular members. The Cauchy problems for linear nonhomogeneous differential equations with a constant coeffi
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Vaculíková, Ľudmila, and Vladimír Liška. "Singularly Perturbed Linear Neumann Problem with the Characteristic Roots on the Imaginary Axis." Research Papers Faculty of Materials Science and Technology Slovak University of Technology 18, no. 28 (2010): 163–68. http://dx.doi.org/10.2478/v10186-010-0020-4.

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Singularly Perturbed Linear Neumann Problem with the Characteristic Roots on the Imaginary Axis We investigate the problem of existence and asymptotic behavior of solutions for the singularly perturbed linear Neumann problem <img src="/fulltext-image.asp?format=htmlnonpaginated&src=C6551P41673P4147_html\Journal10186_Volume18_Issue28_20_paper.gif" alt=""/> Our approach relies on the analysis of integral equation equivalent to the problem above.
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Mane, Shilpkala T., and Ram Kishun Lodhi. "Quartic B-Spline Technique for Third-Order Linear Singularly Perturbed Boundary Value Problem with Discontinuous Source Term." International Journal of Mathematical, Engineering and Management Sciences 10, no. 4 (2024): 1178–91. https://doi.org/10.33889/ijmems.2025.10.4.056.

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In this paper, we developed an effective computational technique for addressing third-order linear singularly perturbed problems having the source term discontinuous. Boundary or interior layers are frequently present in singular perturbation issues, making traditional numerical techniques more challenging. Here, we present a quartic B-spline method (QBSM) for the approximate solution of the third-order singularly perturbed boundary value problem, improving both the accuracy and efficiency of the solutions. In addition, the proposed method's convergence and error are investigated. The performa
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Tsekhan, Olga. "Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation." Axioms 8, no. 2 (2019): 71. http://dx.doi.org/10.3390/axioms8020071.

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The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditi
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Grossmann, Christian, Lars Ludwig, and Hans-Görg Roos. "Layer-adapted methods for a singularly perturbed singular problem." Computational Methods in Applied Mathematics 11, no. 2 (2011): 192–205. http://dx.doi.org/10.2478/cmam-2011-0010.

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Abstract In the present paper we analyze linear finite elements on a layer adapted mesh for a boundary value problem characterized by the overlapping of a boundary layer with a singularity. Moreover, we compare this approach numerically with the use of adapted basis functions, in our case modified Bessel functions. It turns out that as well adapted meshes as adapted basis functions are suitable where for our one-dimensional problem adapted bases work slightly better.
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Akmatov, A. "Investigation of Solutions to a System of Singularly Perturbed Differential Equations." Bulletin of Science and Practice 8, no. 5 (2022): 15–23. http://dx.doi.org/10.33619/2414-2948/78/01.

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Solutions of linear systems of singularly perturbed differential equations are investigated in the work, in the case when the matrix function had multiple eigenvalues. And also in the study of solutions to a system of singularly perturbed differential equations, we apply the level line method. We define a stable and unstable interval. We take the starting point in stable intervals. Passing to the complex domain, we define the domain that we study for solutions of the problem under consideration. We divide the defined areas near the singular point into several areas. In each area, we estimate t
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Dissertations / Theses on the topic "Linear singularly perturbed problem"

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Howe, Sei. "Upper and lower bounds for singularly perturbed linear quadratic optimal control problems." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/54758.

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The question of how to optimally control a large scale system is widely considered to be difficult to solve due to the size of the problem. This difficulty is further compounded when a system exhibits a two time-scale structure where some components evolve slowly and others evolve quickly. When this occurs, the optimal control problem is regarded as singularly perturbed with a perturbation parameter epsilon representing the ratio of the slow time-scale to the fast time-scale. As epsilon goes to zero, the system becomes stiff resulting in a computationally intractable problem. In this thesis, w
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Tang, Ying. "Stability analysis and Tikhonov approximation for linear singularly perturbed hyperbolic systems." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAT054/document.

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Les dynamiques des systèmes modélisés par des équations aux dérivées partielles (EDPs) en dimension infinie sont largement liées aux réseaux physiques. La synthèse de la commande et l'analyse de la stabilité de ces systèmes sont étudiées dans cette thèse. Les systèmes singulièrement perturbés, contenant des échelles de temps multiples sont naturels dans les systèmes physiques avec des petits paramètres parasitaires, généralement de petites constantes de temps, les masses, les inductances, les moments d'inertie. La théorie des perturbations singulières a été introduite pour le contrôle à la fin
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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.

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A singularly perturbed reaction-diffusion model problem is considered, and the choice of an appropriate norm is discussed. Particular emphasis is given to the energy norm. Certain prejudices against this norm are investigated and disproved. Moreover, an adaptive finite element algorithm is presented which exhibits an optimal error decrease in the energy norm in some simple numerical experiments. This underlines the suitability of the energy norm.
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Adkins, 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.

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Kunert, 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.

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Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly
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Grosman, Serguei. "Robust local problem error estimation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600475.

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Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in the discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both the perturbation parameters of the problem and the anisotropy of the mesh. An estimator that has shown to be one of the most reliable for reaction-diffusion problem is the <i>equilibrated residual method</i> and its modification done by
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Blomberg, Magnus. "High Bandwidth Control of a Small Aerial Vehicle." Thesis, Linköpings universitet, Reglerteknik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-119622.

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Small aerial vehicles such as quad-rotors have been widely used commercially, for research and for hobby for the last decade with use still growing. The high interest is mainly due to the vehicles being small, simple, cheap and versatile. Among rigid body dynamics fast dynamics exist cohering to motors and other fast actuators. A linear quadratic control design technique is here investigated. The design technique suggests that the linear quadratic controller can be designed with penalties on the slow states only. The fast dynamics are modeled but the states are not penalised in the linear quad
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Dalla, Riva Matteo. "Potential theoretic methods for the analysis of singularly perturbed problems in linearized elasticity." Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3426270.

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The dissertation is made of two chapters. The first chapter is dedicated to the investigation of some properties of the layer potentials of a constant coefficient elliptic partial differential operator. In the second chapter, we focus our attention to the Lamè equations, which are related to the physic of an isotropic homogeneous elastic body. In particular, in the first chapter, we investigate the dependence of the single layer potential upon perturbation of the density, the support and the coefficients of the corresponding operator. Under some more restrictive assumptions on the operator,
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Kunert, 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.

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The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H^1 seminorm that can be applied to anisotropic finite element meshes. A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably. Furthermore three modifications of these estimators are introduced and discussed. Numerical experiments for all estimators complement and confirm the theoretical results.
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Maddah, 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.

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Dans cette thèse, nous nous sommes intéressés à l'analyse locale de systèmes différentiels linéaires singulièrement perturbés et de systèmes de Pfaff complètement intégrables et multivariés à croisements normaux. De tels systèmes ont une vaste littérature et se retrouvent dans de nombreuses applications. Cependant, leur résolution symbolique est toujours à l'étude. Nos approches reposent sur l'état de l'art de la réduction formelle des systèmes linéaires singuliers d'équations différentielles ordinaires univariées (ODS). Dans le cas des systèmes différentiels linéaires singulièrement perturbés
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Books on the topic "Linear singularly perturbed problem"

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Glizer, Valery Y. Controllability of Singularly Perturbed Linear Time Delay Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65951-6.

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Gajić, Zoran, Djordjija Petkovski, and Xuemin Shen, eds. Singularly Perturbed and Weakly Coupled Linear Control Systems. Springer-Verlag, 1990. http://dx.doi.org/10.1007/bfb0005209.

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Gajić, Zoran. Singularly perturbed and weakly coupled linear control systems: A recursive approach. Springer-Verlag, 1990.

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Myo-Taeg, Lim, ed. Optimal control of singularly perturbed linear systems and applications: High-accuracy techniques. Marcel Dekker, 2001.

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Boglaev, Igor. Domain decomposition in boundary layers for a singularly perturbed parabolic problem. Faculty of Information and Mathematical Sciences, Massey University, 1997.

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Glizer, Valery Y. Controllability of Singularly Perturbed Linear Time Delay Systems. Springer International Publishing AG, 2022.

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Glizer, Valery Y. Controllability of Singularly Perturbed Linear Time Delay Systems. Springer International Publishing AG, 2021.

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Convection Diffusion Problems: An Introduction to Their Analysis and Numerical Solution. American Mathematical Society, 2018.

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Gajic, Zoran. Optimal Control of Singularly Perturbed Linear Systems and Applications. Taylor & Francis Group, 2001.

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Gajic, Zoran. Optimal Control of Singularly Perturbed Linear Systems and Applications. Taylor & Francis Group, 2001.

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Book chapters on the topic "Linear singularly perturbed problem"

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Wasow, Wolfgang. "A Singularly Perturbed Turning Point Problem." In Linear Turning Point Theory. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-1090-0_11.

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Dalla Riva, Matteo, Massimo Lanza de Cristoforis, and Paolo Musolino. "Other Problems with Linear Boundary Conditions in a Domain with a Small Hole." In Singularly Perturbed Boundary Value Problems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76259-9_9.

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Mahendran, R., and V. Subburayan. "Fitted Numerical Method with Linear Interpolation for Third-Order Singularly Perturbed Delay Problems." In Springer Proceedings in Mathematics & Statistics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7546-1_6.

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Nhan, Thái Anh, and Niall Madden. "Cholesky Factorisation of Linear Systems Coming from Finite Difference Approximations of Singularly Perturbed Problems." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25727-3_16.

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Swaminathan, Parthiban, Valarmathi Sigamani, and Franklin Victor. "Numerical Method for a Singularly Perturbed Boundary Value Problem for a Linear Parabolic Second Order Delay Differential Equation." In Springer Proceedings in Mathematics & Statistics. Springer India, 2016. http://dx.doi.org/10.1007/978-81-322-3598-9_7.

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Saminathan, Parthiban, and Franklin Victor. "Numerical Method for a Boundary Value Problem for a Linear System of Partially Singularly Perturbed Parabolic Delay Differential Equations of Reaction-Diffusion Type." In Springer Proceedings in Mathematics & Statistics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7546-1_4.

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Glizer, Valery Y. "Singularly Perturbed Linear Time Delay Systems." In Systems & Control: Foundations & Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-65951-6_2.

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Bauer, S. M., S. B. Filippov, A. L. Smirnov, P. E. Tovstik, and R. Vaillancourt. "Singularly Perturbed Linear Ordinary Differential Equations." In Asymptotic methods in mechanics of solids. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18311-4_4.

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Gajić, Zoran, and Xuemin Shen. "Singularly Perturbed Weakly Coupled Linear Control Systems." In Parallel Algorithms for Optimal Control of Large Scale Linear Systems. Springer London, 1993. http://dx.doi.org/10.1007/978-1-4471-3219-6_10.

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Dalla Riva, Matteo, Massimo Lanza de Cristoforis, and Paolo Musolino. "A Dirichlet Problem in a Domain with Two Small Holes." In Singularly Perturbed Boundary Value Problems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76259-9_10.

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Conference papers on the topic "Linear singularly perturbed problem"

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Chitour, Yacine, Jamal Daafouz, Ihab Haidar, Paolo Mason, and Mario Sigalotti. "Necessary conditions for the stability of singularly perturbed linear systems with switching slow-fast behaviors." In 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024. https://doi.org/10.1109/cdc56724.2024.10886229.

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Myshkov, Stanislav K., and Vladimir V. Karelin. "Minimax control in the singularly perturbed linear-quadratic stabilization problem." In 2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP). IEEE, 2015. http://dx.doi.org/10.1109/scp.2015.7342130.

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Sagara, Muneomi, Hiroaki Mukaidani, and Toru Yamamoto. "Numerical computation of linear quadratic control problem for singularly perturbed stochastic systems." In 2009 International Conference on Networking, Sensing and Control (ICNSC). IEEE, 2009. http://dx.doi.org/10.1109/icnsc.2009.4919367.

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Kodra, Kliti, and Zoran Gajic. "Linear-quadratic-Gaussian problem for a new class of singularly perturbed stochastic systems." In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, 2016. http://dx.doi.org/10.1109/cdc.2016.7799407.

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Gajic, Z., Dj Petkovski, and N. Harkara. "The Recursive Algorithm for the Optimal Static Output Feedback Control Problem of Linear Singularly Perturbed Systems." In 1988 American Control Conference. IEEE, 1988. http://dx.doi.org/10.23919/acc.1988.4789818.

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Radisavljevic-Gajic, Verica. "A Simplified Two-Stage Design of Linear Discrete-Time Feedback Controllers With Applications to Systems With Slow and Fast Modes." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6278.

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In this paper we have shown how to simplify an algorithm for the two stage design of linear feedback controllers by reducing computational requirements. The algorithm is further simplified for linear discrete-time systems with slow and fast modes (multi-time scale systems or singularly perturbed systems) providing independent and accurate designs in slow and fast time scales. The simplified design procedure and its very high accuracy are demonstrated on the eigenvalue assignment problem of a steam power system.
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Edwards Jr., David. "A Numerical Solution of the Semi Linear Singularly Perturbed Boundary Value Problem Using Multi Region Finite Difference Method." In 2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2009. http://dx.doi.org/10.1109/synasc.2009.35.

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Kurina, Galina Alekseevna, and Thi Hoai Nguyen. "On zero order asymptotic solution of singularly perturbed linear - quadratic problems in a critical case." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc23000.

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Shaldanbayev, Amir, Manat Shomanbayeva, and Asylzat Kopzhassarova. "Solution of a singularly perturbed Cauchy problem for linear systems of ordinary differential equations by the method of spectral decomposition." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959704.

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Kurina, Galina A., and Nguyen Thi Hoai. "Projector approach for constructing the zero order asymptotic solution for the singularly perturbed linear-quadratic control problem in a critical case." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5049067.

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Reports on the topic "Linear singularly perturbed problem"

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Ferguson, Warren E., and Jr. Analysis of a Singularly-Perturbed Linear Two-Point Boundary-Value Problem. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada172582.

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Lou, Xi-Cheng, Alan S. Willsky, and George C. Verghese. An Algebraic Approach to Time Scale Analysis of Singularly Perturbed Linear Systems,. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada186040.

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