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Journal of Applied Mathematics, 2012 This paper extends the continuous-time waveform relaxation method to singular perturbation initial value problems. The sufficient conditions for convergence of continuous-time waveform relaxation methods for singular perturbation initial value problems ...
Yongxiang Zhao, Li Li
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Absolutely stable difference scheme for a general class of singular perturbation problems
Advances in Difference Equations, 2020 This paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem
Essam R. El-Zahar +5 more
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Parametric Borel summability for some semilinear system of partial differential equations [PDF]
Opuscula Mathematica, 2015 In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \(n\) independent variables. In [Singular perturbation of linear systems with a regular singularity,
Hiroshi Yamazawa, Masafumi Yoshino
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Singular Perturbations in Viscoelasticity
Rocky Mountain Journal of Mathematics, 1993 We study the singular perturbation for a class of partial integro- differential equations in viscoelasticity of the form \[ \rho u^ \rho_{tt} (t,x) = Eu^ \rho_{xx} (t,x) + \int ^ t _{-\infty} a (t-s) u^ \rho_{xx} (s,x) ds + \rho g (t,x) + f (x),\tag{a} \] when the density \(\rho\) of the material goes to zero. We will prove that when \(\rho \to 0\) the
Grimmer, Ronald, Liu, Hetao
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The effect of arbitrarily small rigidity on the free oscillations of the Earth
Annals of Geophysics, 1997 The system of propagator equations for an elastic solid becomes singular as the shear modulus becomes vanishingly small. In computational applications there is severe loss of precision as the limit of zero shear modulus is approached.
F. Gilbert
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Dynamic model reduction: An overview of available techniques with application to power systems [PDF]
Serbian Journal of Electrical Engineering, 2012 This paper summarises the model reduction techniques used for the reduction of large-scale linear and nonlinear dynamic models, described by the differential and algebraic equations that are commonly used in control theory. The groups of methods
Đukić Savo D., Sarić Andrija T.
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Asymptotics of conduction velocity restitution in models of electrical excitation in the heart [PDF]
, 2011 We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability.
Simitev, R.D., Biktashev, V.N.
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Existence of Solitary Waves in a Perturbed KdV-mKdV Equation
Journal of Mathematics, 2021 In this paper, we establish the existence of a solitary wave in a KdV-mKdV equation with dissipative perturbation by applying the geometric singular perturbation technique and Melnikov function.
Chengqun Li, Minzhi Wei, Yuanhua Lin
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Principal component analysis and perturbation theory–based robust damage detection of multifunctional aircraft structure [PDF]
, 2013 A fundamental problem in structural damage detection is to define an efficient feature to calculate a damage index. Furthermore, due to perturbations from various sources, we also need to define a rigorous threshold whose overtaking indicates the ...
HAJRYA, Rafik, MECHBAL, Nazih
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Relative Perturbation Theory for Hyperbolic Singular Value Problem [PDF]
, 2002 We give relative perturbation bounds for singular values and perturbation bounds for singular subspaces of a hyperbolic singular value problem for the pair (G; J), where G is a full rank matrix and J is a diagonal matrix of ...
Ivan Slapnicar +3 more
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