Results 141 to 150 of about 569 (183)

Singularly Perturbed Systems of Volterra Equations

Journal of Applied Analysis, 2002
This paper studies the behaviour of the solution \(u(t,\varepsilon)\) of the system of Volterra integral equations \[ \varepsilon u(t) = f(t) + \int_0^t A(t,s)u(s)\,ds, \quad 0 \leq t \leq T, \] as the positive parameter \(\epsilon\) tends to zero. Both \(f\) and \(A\) are continuous, and the eigenvalues of \(A(t,t)\) are supposed to be negative.
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On a Class of Singularly Perturbed Parabolic Equations

ZAMM, 2001
Summary: A method of matched asymptotic expansions has been used to construct an \(n\)-term uniformly valid approximate solution for an initial-value problem of a linear singularly perturbed parabolic equation exhibiting an internal layer behavior. It is shown that each internal layer function caused by a non-smooth initial data can be described by an \
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Singularly Perturbed Volterra Integral Equations II

SIAM Journal on Applied Mathematics, 1987
The authors extend the formal methodology for the asymptotic analysis of singularly perturbed Volterra integral equations developed by themselves [ibid. 47, 1-14 (1987; Zbl 0616.45009)] to several problems of the form \[ \epsilon (a(\epsilon)u'(t)+b(\epsilon)u(t))=\int^{t}_{0}k(t,s;\epsilon)f[u(s),s ;\epsilon]\quad ds+f(t;\epsilon),\quad t\geq 0 ...
Angell, J. S., Olmstead, W. E.
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A Class of Singularly Perturbed Semilinear Elliptic Equations

Journal of Partial Differential Equations, 2002
A singularly perturbed problem for semilinear elliptic equations in a strip domain in \(\mathbb R^n\) is considered. The existence and asymptotic behaviour of the solution is established under appropriate conditions. A formal solution in the form of power series with respect to the perturbation parameter is, thereafter using a comparison theorem and ...
Ge, Hongxia, Ding, Li
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Singularly perturbed difference equations

Journal of Difference Equations and Applications, 1999
Comstock and Hsiao have given a method for constructing asymptotic approximations for singularly perturbed linear difference equations with two point boundary conditions and for verifying the corre...
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Singularly Perturbed Volterra Integro-differential Equations

Quaestiones Mathematicae, 2002
Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations.
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Asymptotic solutions for singularly perturbed Boussinesq equations

Applied Mathematics and Computation, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
John Haussermann, Robert A. Van Gorder
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On the Theory of Difference Schemes for Singularly Perturbed Equations

Differential Equations, 2004
A two-point boundary value problem for a linear singularly perturbed reaction-diffusion equation is considered. A classical three-point difference scheme, on an arbitrary nonuniform grid, is used for the numerical solution of this problem. Estimates of the Green function of the grid problem are performed.
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Singularly perturbed problems in partial differential equations: a survey

Applied Mathematics and Computation, 2003
The authors survey a surprisingly large amount of material on singularly perturbed partial differential equations and which indeed can serve as an introduction to some of the ideas and methods of singular perturbation theory. This paper limits its coverage to some standard singular perturbation models considered by various workers and the methods ...
Mohan K. Kadalbajoo, Kailash C. Patidar
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Bifurcation singularities of a singularly perturbed equation with delay

Siberian Mathematical Journal, 1999
The singularly perturbed equation with delay of the form \[ \varepsilon \frac{dx}{dt}+x(t-\varepsilon h)=F(x(t-1)) \] is considered.
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