Gotowe bibliografie tematyczne / Singularly Perturbed Differential Equation

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Gotowa bibliografia na temat „Singularly Perturbed Differential Equation”

Autor: Grafiati

Data publikacji: 6 września 2023

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Artykuły w czasopismach na temat "Singularly Perturbed Differential Equation"

Kanth, A. S. V. Ravi, i P. Murali Mohan Kumar. "A Numerical Technique for Solving Nonlinear Singularly Perturbed Delay Differential Equations". Mathematical Modelling and Analysis 23, nr 1 (12.02.2018): 64–78. http://dx.doi.org/10.3846/mma.2018.005.

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This paper presents a numerical technique for solving nonlinear singu- larly perturbed delay differential equations. Quasilinearization technique is applied to convert the nonlinear singularly perturbed delay differential equation into a se- quence of linear singularly perturbed delay differential equations. An exponentially fitted spline method is presented for solving sequence of linear singularly perturbed delay differential equations. Error estimates of the method is discussed. Numerical examples are solved to show the applicability and efficiency of the proposed scheme.

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Yüzbaşı, Şuayip, i Mehmet Sezer. "Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations". Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/493204.

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This paper deals with the singularly perturbed delay differential equations under boundary conditions. A numerical approximation based on the exponential functions is proposed to solve the singularly perturbed delay differential equations. By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear algebraic equations. Also, an error analysis technique based on the residual function is introduced for the method. Four examples are considered to demonstrate the performance of the proposed scheme, and the results are discussed.

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Battelli, Flaviano, i Michal Fečkan. "Periodic Solutions in Slowly Varying Discontinuous Differential Equations: The Generic Case". Mathematics 9, nr 19 (2.10.2021): 2449. http://dx.doi.org/10.3390/math9192449.

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We study persistence of periodic solutions of perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular periodic solution. The results of this paper are motivated by a result of Holmes and Wiggins where the authors considered a two dimensional Hamiltonian family of smooth systems depending on a scalar variable which is the solution of a singularly perturbed equation.

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YUZBASI, SUAYIP, i NURCAN BAYKUS SAVASANERIL. "HERMITE POLYNOMIAL APPROACH FOR SOLVING SINGULAR PERTURBATED DELAY DIFFERENTIAL EQUATIONS". Journal of Science and Arts 20, nr 4 (30.12.2020): 845–54. http://dx.doi.org/10.46939/j.sci.arts-20.4-a06.

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In this study, a collocation approach based on the Hermite polyomials is applied to solve the singularly perturbated delay differential eqautions by boundary conditions. By means of the matix relations of the Hermite polynomials and the derivatives of them, main problem is reduced to a matrix equation. And then, collocation points are placed in equation of the matrix. Hence, the singular perturbed problem is transformed into an algebraic system of linear equations. This system is solved and thus the coefficients of the assumed approximate solution are determined. Numerical applications are made for various values of N.

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Et. al., M. Adilaxmi ,. "Solution Of Singularly Perturbed Delay Differential Equations Using Liouville Green Transformation". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, nr 4 (11.04.2021): 325–35. http://dx.doi.org/10.17762/turcomat.v12i4.510.

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This paper envisages the use of Liouville Green Transformation to find the solution of singularly perturbed delay differential equations. First, using Taylor series, the given singularly perturbed delay differential equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. The method is demonstrated by implementing several model examples by taking various values for the delay parameter and perturbation parameter.

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Duressa, Gemechis File, Imiru Takele Daba i Chernet Tuge Deressa. "A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations". Mathematics 11, nr 5 (22.02.2023): 1108. http://dx.doi.org/10.3390/math11051108.

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This review paper contains computational methods or solution methodologies for singularly perturbed differential difference equations with negative and/or positive shifts in a spatial variable. This survey limits its coverage to singular perturbation equations arising in the modeling of neuronal activity and the methods developed by numerous researchers between 2012 and 2022. The review covered singularly perturbed ordinary delay differential equations with small or large negative shift(s), singularly perturbed ordinary differential–differential equations with mixed shift(s), singularly perturbed delay partial differential equations with small or large negative shift(s) and singularly perturbed partial differential–difference equations of the mixed type. The main aim of this review is to find out what numerical and asymptotic methods were developed in the last ten years to solve such problems. Further, it aims to stimulate researchers to develop new robust methods for solving families of the problems under consideration.

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Bobodzhanov, A., B. Kalimbetov i N. Pardaeva. "Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating cosine". Journal of Mathematics and Computer Science 32, nr 01 (21.07.2023): 74–85. http://dx.doi.org/10.22436/jmcs.032.01.07.

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In this paper, we consider a singularly perturbed integro-differential equation with a rapidly oscillating right-hand side, which includes an integral operator with a slowly varying kernel. Earlier, singularly perturbed differential and integro-differential equations with rapidly oscillating coefficients were considered. The main goal of this work is to generalize the Lomov's regularization method and to identify the rapidly oscillating right-hand side to the asymptotics of the solution to the original problem.

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Sharip, B., i А. Т. Yessimova. "ESTIMATION OF A BOUNDARY VALUE PROBLEM SOLUTION WITH INITIAL JUMP FOR LINEAR DIFFERENTIAL EQUATION". BULLETIN Series of Physics & Mathematical Sciences 69, nr 1 (10.03.2020): 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 boundary value problems, and also the Green function. With the help of these functions, an analytical formula is obtained for solving a singularly perturbed boundary value problem and it turns out that this solution has an initial zero-order jump at t = 0. It is proved that the solution to the considered singularly perturbed boundary value problem tends to the corresponding unperturbed problem obtained from it under .

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Zhumanazarova, Assiya, i Young Im Cho. "Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem". Mathematics 8, nr 2 (7.02.2020): 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. Analytical formulae for the solutions and asymptotic estimates of the singularly perturbed problem are obtained. Furthermore, a modified degenerate boundary value problem has been constructed, and it was stated that the solution of the original singularly perturbed boundary value problem tends to this modified problem’s solution.

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Vrábeľ, Róbert. "Asymptotic behavior of $T$-periodic solutions of singularly perturbed second-order differential equation". Mathematica Bohemica 121, nr 1 (1996): 73–76. http://dx.doi.org/10.21136/mb.1996.125946.

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Rozprawy doktorskie na temat "Singularly Perturbed Differential Equation"

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.

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Magister Scientiae - MSc
Many 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.

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Song, Xuefeng. "Dynamic modeling issues for power system applications". Texas A&M University, 2003. http://hdl.handle.net/1969.1/1591.

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Power system dynamics are commonly modeled by parameter dependent nonlinear differential-algebraic equations (DAE) x p y x f ) and 0 = p y x g ) . Due to (,, (,, the algebraic constraints, we cannot directly perform integration based on the DAE. Traditionally, we use implicit function theorem to solve for fast variables y to get a reduced model in terms of slow dynamics locally around x or we compute y numerically at each x . However, it is well known that solving nonlinear algebraic equations analytically is quite difficult and numerical solution methods also face many uncertainties since nonlinear algebraic equations may have many solutions, especially around bifurcation points. In this thesis, we apply the singular perturbation method to model power system dynamics in a singularly perturbed ODE (ordinary-differential equation) form, which makes it easier to observe time responses and trace bifurcations without reduction process. The requirements of introducing the fast dynamics are investigated and the complexities in the procedures are explored. Finally, we propose PTE (Perturb and Taylors expansion) technique to carry out our goal to convert a DAE to an explicit state space form of ODE. A simplified unreduced Jacobian matrix is also introduced. A dynamic voltage stability case shows that the proposed method works well without complicating the applications.

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Iragi, Bakulikira. "On the numerical integration of singularly perturbed Volterra integro-differential equations". University of the Western Cape, 2017. http://hdl.handle.net/11394/5669.

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Magister Scientiae - MSc
Efficient 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.

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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.

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This thesis addresses the existence and stability of localised solutions in some nonstandard systems of partial differential equations. In particular, it locates the linearised spectrum of a Keller-Segel model for bacterial chemotaxis with logarithmic chemosensitivity, establishes the existence of travelling wave solutions to the Gatenby-Gawlinski model for tumour invasion with the acid-mediation hypothesis using geometric singular perturbation theory, and formulates the Evans function for a trivial defect solution in a general reaction diffusion equation with an added heterogeneous defect. Extending the analysis to these non-standard problems provides a foundation and insight for more general dynamical systems.

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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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Höhne, 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.

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Be it in the weather forecast or while swimming in the Baltic Sea, in almost every aspect of every day life we are confronted with flow phenomena. A common model to describe the motion of viscous incompressible fluids are the Navier-Stokes equations. These equations are not only relevant in the field of physics, but they are also of great interest in a purely mathematical sense. One of the difficulties of the Navier-Stokes equations originates from a non-linear term. In this thesis, we consider the Oseen equations as a linearisation of the Navier-Stokes equations. We restrict ourselves to the two-dimensional case. Our domain will be the unit square. The aim of this thesis is to find a suitable numerical method to overcome known instabilities in discretising these equations. One instability arises due to layers of the analytical solution. Another instability comes from a divergence constraint, where one gets poor numerical accuracy when the irrotational part of the right-hand side of the equations is large. For the first cause, we investigate the layer behaviour of the analytical solution of the corresponding stream function of the problem. Assuming a solution decomposition into a smooth part and layer parts, we create layer-adapted meshes in Chapter 3. Using these meshes, we introduce a numerical method for equations whose solutions are of the assumed structure in Chapter 4. To reduce the instability caused by the divergence constraint, we add a grad-div stabilisation term to the standard Galerkin formulation. We consider Taylor-Hood elements and elements with a discontinous pressure space. We can show that there exists an error bound which is independent of our perturbation parameter and get information about the convergence rate of the method. Numerical experiments in Chapter 5 confirm our theoretical results.

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Reibiger, 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.

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It is well-known that the solution of a so-called singularly perturbed differential equation exhibits layers. These are small regions in the domain where the solution changes drastically. These layers deteriorate the convergence of standard numerical algorithms, such as the finite element method on a uniform mesh. In the past many approaches were developed to overcome this difficulty. In this context it was very helpful to understand the structure of the solution - especially to know where the layers can occur. Therefore, we have a lot of analysis in the literature concerning the properties of solutions of such problems. Nevertheless, this field is far from being understood conclusively. More recently, there is an increasing interest in the numerics of optimal control problems subject to a singularly perturbed convection-diffusion equation and box constraints for the control. However, it is not much known about the solutions of such optimal control problems. The proposed solution methods are based on the experience one has from scalar singularly perturbed differential equations, but so far, the analysis presented does not use the structure of the solution and in fact, the provided bounds are rather meaningless for solutions which exhibit boundary layers, since these bounds scale like epsilon^(-1.5) as epsilon converges to 0. In this thesis we strive to prove bounds for the solution and its derivatives of the optimal control problem. These bounds show that there is an additional layer that is weaker than the layers one expects knowing the results for scalar differential equation problems, but that weak layer deteriorates the convergence of the proposed methods. In Chapter 1 and 2 we discuss the optimal control problem for the one-dimensional case. We consider the case without control constraints and the case with control constraints separately. For the case without control constraints we develop a method to prove bounds for arbitrary derivatives of the solution, given the data is smooth enough. For the latter case we prove bounds for the derivatives up to the second order. Subsequently, we discuss several discretization methods. In this context we use special Shishkin meshes. These meshes are piecewise equidistant, but have a very fine subdivision in the region of the layers. Additionally, we consider different ways of discretizing the control constraints. The first one enforces the compliance of the constraints everywhere and the other one enforces it only in the mesh nodes. For each proposed algorithm we prove convergence estimates that are independent of the parameter epsilon. Hence, they are meaningful even for small values of epsilon. As a next step we turn to the two-dimensional case. To be able to adapt the proofs of Chapter 2 to this case we require bounds for the solution of the scalar differential equation problem for a right hand side f only in W^(1,infty). Although, a lot of results for this problem can be found in the literature but we can not apply any of them, because they require a smooth right hand side f in C^(2,alpha) for some alpha in (0,1). Therefore, we dedicate Chapter 3 to the analysis of the scalar differential equations problem only using a right hand side f that is not very smooth. In Chapter 4 we strive to prove bounds for the solution of the optimal control problem in the two dimensional case. The analysis for this problem is not complete. Especially, the characteristic layers induce subproblems that are not understood completely. Hence, we can not prove sharp bounds for all terms in the solution decomposition we construct. Nevertheless, we propose a solution method. Numerical results indicate an epsilon-independent convergence for the considered examples - although we are not able to prove this.

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Kaiser, Klaus [Verfasser], Sebastian [Akademischer Betreuer] Noelle, Jochen [Akademischer Betreuer] Schütz i 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.

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Reibiger, Christian [Verfasser], Hans-Görg [Akademischer Betreuer] Roos i 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.

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Roos, Hans-Görg, i 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.

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We consider a system of weakly coupled singularly perturbed convection-diffusion equations with multiple scales. Based on sharp estimates for first order derivatives, Linß [T. Linß, Computing 79 (2007) 23–32.] analyzed the upwind finite-difference method on a Shishkin mesh. We derive such sharp bounds for second order derivatives which show that the coupling generates additional weak layers. Finally, we prove the first robust convergence result for the Galerkin finite element method for this class of problems on modified Shishkin meshes introducing a mesh grading to cope with the weak layers. Numerical experiments support our theory.

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Książki na temat "Singularly Perturbed Differential Equation"

Scroggs, Jeffrey S. Shock-layer bounds for a singularly perturbed equation. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1990.

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Roos, Hans-Görg, Martin Stynes i Lutz Tobiska. Numerical Methods for Singularly Perturbed Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-03206-0.

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F, Mishchenko E., red. Asymptotic methods in singularly perturbed systems. New York: Consultants Bureau, 1994.

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Homogenization in time of singularly perturbed mechanical systems. Berlin: Springer-Verlag, 1998.

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Mazʹi︠a︡, V. G. Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Basel: Birkhäuser Verlag, 2000.

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

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Wang, Kelei. Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33696-6.

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Roos, Hans-Görg. Numerical methods for singularly perturbed differential equations: Convection-diffusion and flow problems. Berlin: Springer-Verlag, 1996.

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Asymptotic behavior of monodromy: Singularly perturbed differential equations on a Riemann surface. Berlin: Springer-Verlag, 1991.

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Mazia, V. G. Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Basel: Springer Basel, 2000.

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Części książek na temat "Singularly Perturbed Differential Equation"

Sharkovsky, A. N., Yu L. Maistrenko i E. Yu Romanenko. "Singularly Perturbed Differential-Difference Equations". W Difference Equations and Their Applications, 239–72. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1763-0_10.

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O’Malley, Robert E. "Singularly Perturbed Initial Value Problems". W Singular Perturbation Methods for Ordinary Differential Equations, 22–91. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-0977-5_2.

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O’Malley, Robert E. "Singularly Perturbed Boundary Value Problems". W Singular Perturbation Methods for Ordinary Differential Equations, 92–200. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-0977-5_3.

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Bauer, S. M., S. B. Filippov, A. L. Smirnov, P. E. Tovstik i R. Vaillancourt. "Singularly Perturbed Linear Ordinary Differential Equations". W Asymptotic methods in mechanics of solids, 155–237. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18311-4_4.

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Wang, Kelei. "The Limit Equation of a Singularly Perturbed System". W Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations, 95–105. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33696-6_7.

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Fruchard, Augustin, i Reinhard Schäfke. "Composite Expansions and Singularly Perturbed Differential Equations". W Composite Asymptotic Expansions, 81–118. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34035-2_5.

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Haber, S., i N. Levinson. "A Boundary Value Problem for A Singularly Perturbed Differential Equation". W Selected Papers of Norman Levinson, 376–83. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-5332-7_35.

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Levinson, N. "A Boundary Value Problem for A Singularly Perturbed Differential Equation". W Selected Papers of Norman Levinson, 384–95. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-5332-7_36.

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Haber, S., i N. Levinson. "A Boundary Value Problem for a Singularly Perturbed Differential Equation". W Selected Papers of Norman Levinson Volume 1, 376–83. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-5341-9_35.

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Levinson, N. "A Boundary Value Problem for a Singularly Perturbed Differential Equation". W Selected Papers of Norman Levinson Volume 1, 384–95. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-5341-9_36.

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Streszczenia konferencji na temat "Singularly Perturbed Differential Equation"

GELFREICH, V., i L. M. LERMAN. "SLOW MANIFOLDS IN A SINGULARLY PERTURBED HAMILTONIAN SYSTEM". W Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0146.

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Thang Nguyen i Zoran Gajic. "Solving the singularly perturbed matrix differential Riccati equation: A Lyapunov equation approach". W 2010 American Control Conference (ACC 2010). IEEE, 2010. http://dx.doi.org/10.1109/acc.2010.5530936.

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Arora, Geeta, i Mandeep Kaur. "Numerical simulation of singularly perturbed differential equation with small shift". W RECENT ADVANCES IN FUNDAMENTAL AND APPLIED SCIENCES: RAFAS2016. Author(s), 2017. http://dx.doi.org/10.1063/1.4990346.

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WARD, MICHAEL J. "SPIKES FOR SINGULARLY PERTURBED REACTION-DIFFUSION SYSTEMS AND CARRIER’S PROBLEM". W Differential Equations & Asymptotic Theory in Mathematical Physics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702395_0003.

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Butuzov, Valentin Fedorovich. "Singularly perturbed ODEs with multiple roots of the degenerate equation". W International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Moscow: Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc22964.

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Demir, Duygu Dönmez, i Erhan Koca. "The shooting method for the second order singularly perturbed differential equation". W INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952091.

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Yadav, S., i S. Ganesan. "SPDE-ConvNet: Predict stabilization parameter for Singularly Perturbed Partial Differential Equation". W 8th European Congress on Computational Methods in Applied Sciences and Engineering. CIMNE, 2022. http://dx.doi.org/10.23967/eccomas.2022.258.

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DOELMAN, A., D. IRON i Y. NISHIURA. "EDGE BIFURCATIONS IN SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS: A CASE STUDY". W Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0130.

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Drǎgan, Vasile F., i Achim Ioniţǎ. "Exponential stability for singularly perturbed systems with state delays". W The 6'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 1999. http://dx.doi.org/10.14232/ejqtde.1999.5.6.

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Macutan, Y. O. "Formal solutions of scalar singularly-perturbed linear differential equations". W the 1999 international symposium. New York, New York, USA: ACM Press, 1999. http://dx.doi.org/10.1145/309831.309879.

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Raporty organizacyjne na temat "Singularly Perturbed Differential Equation"

Yan, Xiaopu. Singularly Perturbed Differential/Algebraic Equations. Fort Belvoir, VA: Defense Technical Information Center, październik 1994. http://dx.doi.org/10.21236/ada288365.

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Flaherty, Joseph E., i Robert E. O'Malley. Asymptotic and Numerical Methods for Singularly Perturbed Differential Equations with Applications to Impact Problems. Fort Belvoir, VA: Defense Technical Information Center, maj 1986. http://dx.doi.org/10.21236/ada169251.

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