Results 161 to 170 of about 13,060 (202)

Discretization of the semilinear singularly perturbed problem

Nonlinear Analysis: Theory, Methods & Applications, 1997
The authors discuss the construction of a spline function for a class of singularly perturbed singular problems: \[ -\varepsilon^2 x^{2\alpha} u'' (x) + b(x,u)=0, \quad x \in (0,1), \quad u(0)=u(1)=0 \tag{1} \] with parameter \(\alpha \in [0, 0.5) \) and a perturbation parameter \(\varepsilon \in (0, \varepsilon_0 ]\), \(\varepsilon_0 \ll 1\).
Uzelac, Zorica, Surla, Katarina
openaire   +1 more source

Nonlinear singularly perturbed problems of ultra parabolic equations

Applied Mathematics and Mechanics, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Surong, Mo, Jiaqi
openaire   +1 more source

Singularly perturbed boundary value problems

Acta Mathematicae Applicatae Sinica, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Some singular singularly-perturbed problems. II.

1999
Summary: This paper continuous part I published in the previous number of the same volume. For the corresponding summary see [ibid. 15, No. 3, 260--271 (1999; Zbl 0968.34015)].
Chang, K. W., Meng, J.
openaire   +2 more sources

Singularly Perturbed Boundary Value Problems

1991
Consider the two-point problem ey”+a(x)y’+b(x)y=f(x) on 0≤x≤1 where a(x)>0 and with the boundary values y(0) and y(1) prescribed. We shall suppose that a, b, and f are arbitrarily smooth, and we shall prove that the asymptotic solution will exist, be unique, and have the form $$y\left( {x,\varepsilon } \right) = Y\left( {x,\varepsilon } \right ...
openaire   +1 more source

On Nonlinear Singularly Perturbed Initial Value Problems

SIAM Review, 1988
The author studies the singular perturbation initial value problem for the nonlinear system \(x'=f(x,y,t,\epsilon),\) \(\epsilon y'=g(x,y,t,\epsilon)\) on a bounded interval \([0,1]\) with smooth vector functions \(f\) and \(g\) of dimensions \(m\) and \(n\) respectively and with prescribed vector function \(x(0),y(0)\).
openaire   +1 more source

Singularly perturbed initial value problems

1974
£y" + f(x,y,y',6) = O, 0 0 is a small parameter and "prime" denotes differentiation with respect to x. We shall formulate conditions under which the problem (i.i), (1.2) has a unique solution y(x, e) existing on the entire interval [0,b], for e sufficiently small. We shall also obtain explicit bounds on y(x,E) and y' (x,e) as g + 0. In particular, we
openaire   +1 more source

Singularly Perturbed Optimal Control Problems. I: Convergence

SIAM Journal on Control and Optimization, 1976
The problem studied is as follows: when does the full solution of minimizing $x^0 (T)$, given \[\begin{gathered} \dot x(t) = f(x(t),y(t),u(t)),\quad u(t) \in U, \hfill \\ \varepsilon \dot y(t) = g(x(t),y(t),u(t)),\quad 0 \leqq t \leqq T, \hfill \\ \end{gathered} \] with boundary conditions on x and y, converge in some sense to the reduced solution of ...
openaire   +1 more source

Singularly Perturbed Initial Value Problems

1991
Readers should refer to Murray (1977) and to earlier chemical engineering literature [especially Bowen et al. (1963) and Heinekin et al. (1967)] for experts’ explanations of the significance of the pseudo-steady-state hypothesis in biochemistry. The theory of Michaelis and Menton (1913) and Briggs and Haldane (1925) concerns a substrate S being ...
openaire   +1 more source

Singularly perturbed problems with double singularity

Mathematical Notes, 1997
The author deals with systems of linear differential equations \[ \varepsilon^{m_1}\bigl(\delta_0(x)+\varepsilon\bigr)^{m_2}{dy\over dx}=A(x,\varepsilon)y+f(x), \] with \(\delta_0(x)>0\) for \(x\in(0,1)\), \(\delta_0 (0)=\delta_0(1)=0\), \(m_1,m_2\) are positive integers (which determine the two singularities \(x=0\) and \(x=1\), respectively) and the ...
openaire   +2 more sources