Results 161 to 170 of about 57,321 (196)
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Acta Mathematica Scientia, 1992
The authors construct the asymptotic expansion of the solution of a singularly perturbed boundary value problem for a quasilinear higher order ordinary differential equation with three small parameters (two singular perturbation parameters in the operator and one in the boundary conditions). The asymptotic method of Vishik and Lyusternik is applied. An
Lin, Zongchi, Lin, Surong
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The authors construct the asymptotic expansion of the solution of a singularly perturbed boundary value problem for a quasilinear higher order ordinary differential equation with three small parameters (two singular perturbation parameters in the operator and one in the boundary conditions). The asymptotic method of Vishik and Lyusternik is applied. An
Lin, Zongchi, Lin, Surong
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SINGULAR PERTURBATIONS OF ORDINARY DIFFERENTIAL EQUATIONS
1961Abstract : A discussion is presented concerning the perturbation method for ordinary differential equations with a small parameter epsilon. As illustrations of this procedure, use of the Neumann series and the Fredholm expansion is made. The solution of the eigenvalue problem is made for an ordinary differential equation as a power series in epsilon.
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Journal of Education for Pure Science- University of Thi-Qar, 2021
In This paper deals with the study of singularity perturbed ordinary differential equation, and is considered the basis for obtaining the system of differential algebraic equations. In this study the we use implicit function theorem to solve for fast variable y to get a reduced model in terms of slow dynamics locally around x.
Dr.Kamal Hamid Yasser Al-Yassery +1 more
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In This paper deals with the study of singularity perturbed ordinary differential equation, and is considered the basis for obtaining the system of differential algebraic equations. In this study the we use implicit function theorem to solve for fast variable y to get a reduced model in terms of slow dynamics locally around x.
Dr.Kamal Hamid Yasser Al-Yassery +1 more
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A collocation approximation of singularly perturbed second order ordinary differential equation
International Journal of Computer Mathematics, 1991This paper concerns the numerical solutions of two-point singularly perturbed boundary value problems for second order ordinary differential equations. For the linear problem, Canonical polynomials are constructed as new basis for collocation solution in the smooth region which is superposed with an exponential function in the boundary layer region ...
O. A. Taiwo, P. Onumanyi
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On the Estimation of Small Perturbations in Ordinary Differential Equations
1983The essential subject of this work is concerned with those problems represented by a system of ordinary differential equations involving one or several small perturbing functions to be determined in order to obtain either a solution given in advance (control problems) or a solution that approximates a set of measurements that may be affected by random ...
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Acta Mathematica Scientia, 1988
We obtain some results about the convergence of solutions of the boundary value problems of the third order nonlinear ordinary differential equation with a small parameter \(\epsilon >0:\) (1) \(\epsilon x\prime''=f(t,x,x',x'',\epsilon)\), \((2_ i)\) \(x^{(i)}(0)=0\), \(x(1)=0\), \(x'(1)=0\) \((i=0,1,2)\) to a solution of their reduced problem \(u ...
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We obtain some results about the convergence of solutions of the boundary value problems of the third order nonlinear ordinary differential equation with a small parameter \(\epsilon >0:\) (1) \(\epsilon x\prime''=f(t,x,x',x'',\epsilon)\), \((2_ i)\) \(x^{(i)}(0)=0\), \(x(1)=0\), \(x'(1)=0\) \((i=0,1,2)\) to a solution of their reduced problem \(u ...
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SIAM Journal on Mathematical Analysis, 1984
Asymptotic integration of a linear differential equation \[ x^{(n)}+[a_ 1+p_ 1(t)]x^{(n-1)}+...+[a_ n+p_ n(t)]x=0 \] is considered under conditions that the integrals \(\int^{\infty}p_ k(t)e^{ct}t^ qdt\) (where c and q are nonnegative constants) converge (perhaps relatively).
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Asymptotic integration of a linear differential equation \[ x^{(n)}+[a_ 1+p_ 1(t)]x^{(n-1)}+...+[a_ n+p_ n(t)]x=0 \] is considered under conditions that the integrals \(\int^{\infty}p_ k(t)e^{ct}t^ qdt\) (where c and q are nonnegative constants) converge (perhaps relatively).
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Journal of Mathematical Sciences, 2019
Consider the two-dimensional system of singularly perturbed differential equations \[\begin{aligned}\varepsilon^2\frac{d^2u}{dx^2} & =h(x)(u-\varphi(v,x))^2-\varepsilon F_1(u,v,x,\varepsilon), \\ \varepsilon\frac{d^2v}{dx^2} & =f(u,v,x,\varepsilon)\end{aligned} \tag{1}\] on the interval \([0,1]\) with the boundary conditions \[u(0,\varepsilon)=u^0,\ u ...
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Consider the two-dimensional system of singularly perturbed differential equations \[\begin{aligned}\varepsilon^2\frac{d^2u}{dx^2} & =h(x)(u-\varphi(v,x))^2-\varepsilon F_1(u,v,x,\varepsilon), \\ \varepsilon\frac{d^2v}{dx^2} & =f(u,v,x,\varepsilon)\end{aligned} \tag{1}\] on the interval \([0,1]\) with the boundary conditions \[u(0,\varepsilon)=u^0,\ u ...
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Structural identification with physics-informed neural ordinary differential equations
Journal of Sound and Vibration, 2021Zhilu Lai +2 more
exaly
PERTURBATION OF INVARIANT MANIFOLDS OF ORDINARY DIFFERENTIAL EQUATIONS
1996GEORGE OSIPENKO, EUGENE ERSHOV
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