Results 251 to 260 of about 371,472 (295)

Orthogonal polynomials satisfying fourth order differential equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1981
SynopsisThese polynomials, which are intimately connected with the Legendre, Laguerre and Jacobi polynomials, are orthogonal with respect to Stieltjes weight functions which are absolutely continuous on (− 1, 1), (0, ∞) and (0, 1), respectively, but which have jumps at some of the intervals' ends. Each set satisfies a fourth order differential equation
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Fourth-order partial differential equations for noise removal

IEEE Transactions on Image Processing, 2000
A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the absolute value of the Laplacian of the image intensity function.
You, Yu-Li, Kaveh, M.
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Asymptotic Solutions of a Fourth Order Differential Equation

Studies in Applied Mathematics, 2007
In this paper, we derive uniform asymptotic expansions of solutions to the fourth order differential equation image where x is a real variable and λ is a large positive parameter. The solutions of this differential equation can be expressed in the form of contour integrals, and uniform asymptotic expansions are derived by using the cubic ...
Wong, R., Zhang, H. Y.
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Antiperiodic solutions of fourth‐order impulsive differential equation

Mathematical Methods in the Applied Sciences, 2017
In this paper, the existence of antiperiodic solutions for fourth‐order impulsive differential equation is obtained by variational approaches and results on the auxiliary system. It is interesting that there is no growth restraint on nonlinear terms and impulsive terms.
Yu Tian, Suiming Shang, Qiang Huo
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The generalized differential quadrature rule for fourth‐order differential equations

International Journal for Numerical Methods in Engineering, 2001
AbstractThe generalized differential quadrature rule (GDQR) proposed here is aimed at solving high‐order differential equations. The improved approach is completely exempted from the use of the existing δ‐point technique by applying multiple conditions in a rigorous manner.
Wu, T.Y., Liu, G.R.
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Oscillatory applications of some fourth‐order differential equations

Mathematical Methods in the Applied Sciences, 2020
Fourth‐order advanced differential equations naturally appear in models concerning physical, biological, chemical phenomena applications. The aim of this paper is to study the oscillatory properties of fourth‐order advanced differential equations withp‐Laplacian like operators.
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The Fourth-order Bessel–type Differential Equation

Applicable Analysis, 2004
The Bessel-type functions, structured as extensions of the classical Bessel functions, were defined by Everitt and Markett in 1994. These special functions are derived by linear combinations and limit processes from the classical orthogonal polynomials, classical Bessel functions and the Krall Jacobi-type and Laguerre-type orthogonal polynomials. These
Jyoti Das, W.N. Everitt, D.B. Hinton, L.L. Littlejohn, C. Markett   +4 more
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The Sinc-Galerkin Method for Fourth-Order Differential Equations

SIAM Journal on Numerical Analysis, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Smith, Ralph C., Bogar, Gary A., Bowers, Kenneth L., Lund, John   +3 more
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On oscilatory fourth order nonlinear neutral differential equations – IV

Mathematica Slovaca, 2018
AbstractIn this paper, oscillation of all solutions of fourth order functional differential equations of neutral type of the form$$\begin{array}{} \displaystyle (r(t)(y(t)+p(t)y(t-\tau))'')''+q(t)G(y(t-\sigma))=0 \end{array}$$are studied under the assumption$$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}\text{d}t \lt \infty \end ...
Arun Kumar Tripathy, Rashmi Rekha Mohanta   +1 more
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Fourth-order differential equations for numerator polynomials

Journal of Physics A: Mathematical and General, 1988
We give explicitly the fourth-order differential equation satisfied by the numerator polynomials (associated polynomials) of the classical orthogonal polynomials. The coefficients of the differential equation are at most a quadratic combination of the polynomials \(\sigma\) and \(\tau\) (and their derivatives) defined via the relation \((\sigma \rho)'=\
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