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Relevant bibliographies by topics / Singularly Perturbed Differential Equation

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Academic literature on the topic 'Singularly Perturbed Differential Equation'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Singularly Perturbed Differential Equation"

1

Kanth, A. S. V. Ravi, and P. Murali Mohan Kumar. "A Numerical Technique for Solving Nonlinear Singularly Perturbed Delay Differential Equations." Mathematical Modelling and Analysis 23, no. 1 (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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2

Yüzbaşı, Şuayip, and 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 demonstrat

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3

Battelli, Flaviano, and Michal Fečkan. "Periodic Solutions in Slowly Varying Discontinuous Differential Equations: The Generic Case." Mathematics 9, no. 19 (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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4

YUZBASI, SUAYIP, and NURCAN BAYKUS SAVASANERIL. "HERMITE POLYNOMIAL APPROACH FOR SOLVING SINGULAR PERTURBATED DELAY DIFFERENTIAL EQUATIONS." Journal of Science and Arts 20, no. 4 (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 mad

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5

Et. al., M. Adilaxmi ,. "Solution Of Singularly Perturbed Delay Differential Equations Using Liouville Green Transformation." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 4 (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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6

Duressa, Gemechis File, Imiru Takele Daba, and Chernet Tuge Deressa. "A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations." Mathematics 11, no. 5 (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 pertur

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7

Bobodzhanov, A., B. Kalimbetov, and 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, no. 01 (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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8

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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9

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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10

Vrábeľ, Róbert. "Asymptotic behavior of $T$-periodic solutions of singularly perturbed second-order differential equation." Mathematica Bohemica 121, no. 1 (1996): 73–76. http://dx.doi.org/10.21136/mb.1996.125946.

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