Results 41 to 50 of about 1,801,571 (229)

On a Multigrid Method for Tempered Fractional Diffusion Equations

Fractal and Fractional, 2021
In this paper, we develop a suitable multigrid iterative solution method for the numerical solution of second- and third-order discrete schemes for the tempered fractional diffusion equation.
Linlin Bu, Cornelis W. Oosterlee
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Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation [PDF]

, 2008
The Yablonskii-Vorob'ev polynomials $y_{n}(t)$, which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second
Alan K Common, Andrew N W Hone, Clarkson P A, Clarkson P A, Common A K, Common A K, Common A K, Cresswell C, Fukutani S, Hafev S T, Hamamoto T, Hone A N W, Ince E L, Isojima S, Jones W B, Joshi N, Kajiwara K, Kajiwara K, Kajiwara K, Kajiwara K, Nijhoff F, Ramani A, Satsuma J, Suris Y B, Taneda M, Vorob'ev A P, Yablonskii A I   +26 more
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Positive solutions and iterative approximations of a third order nonlinear neutral delay difference equation

Advances in Difference Equations, 2018
This paper deals with the third order nonlinear neutral delay difference equation with a forced term Δ2(a(n)Δ(x(n)+c(n)x(n−τ)))+f(n,x(n−b1(n)),x(n−b2(n)),…,x(n−bk(n)))=d(n),n≥n0.
Guojing Jiang, Hong Yu, Lili Wang, Liangshi Zhao   +3 more
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Periodic Solutions to a Third-Order Conditional Difference Equation over the Integers

Discrete Dynamics in Nature and Society, 2011
This paper studies a third-order conditional difference equation which is a generalization from the literature. We investigate this equation by transforming it into a first-order system. Finally it is proved that the equation has no period-two (or three)
Li He, Wanping Liu
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On Positive Solutions and Mann Iterative Schemes of a Third Order Difference Equation

Abstract and Applied Analysis, 2014
The existence of uncountably many positive solutions and convergence of the Mann iterative schemes for a third order nonlinear neutral delay difference equation are proved. Six examples are given to illustrate the results presented in this paper.
Zeqing Liu, Heng Wu, Shin Min Kang, Young Chel Kwun   +3 more
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Equivalent resistance of irregular 3 × n Hammock resistor network

Nantong Daxue xuebao. Ziran kexue ban, 2022
The equivalent resistance of a kind of irregular 3 × n Hammock resistor network is studied by the RT-I theory, in which the third order matrix equation and the third order boundary condition equation are established by Kirchhoff′s law and the branch ...
TAN Zhizhong
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Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation

, 1999
We consider the polynomials $\phi_n(z)= \kappa_n (z^n+ b_{n-1} z^{n-1}+ >...)$ orthonormal with respect to the weight $\exp(\sqrt{\lambda} (z+ 1/z)) dz/2 \pi i z$ on the unit circle in the complex plane.
Chie Bing Wang, Fokas A S, Hastings S P, Hisakado M, Jimbo M, Szegö G, Tracy C A, Tracy C A, Tracy C A, Tracy C A   +9 more
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Translationally invariant nonlinear Schrodinger lattices

, 2006
Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed.
Berger A, Dmitriev S V, Dmitriev S V, Dmitry E Pelinovsky, Eilbeck J C Johansson M Vázquez L, Friesecke G, Oxtoby O F, Pankov A, Roy I Dmitriev S V Kevrekidis P G Saxena A, Speight J M, Speight J M, Tovbis A   +11 more
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Representation of solutions of a solvable nonlinear difference equation of second order

Electronic Journal of Qualitative Theory of Differential Equations, 2018
We present a representation of well-defined solutions to the following nonlinear second-order difference equation $$x_{n+1}=a+\frac{b}{x_n}+\frac{c}{x_nx_{n-1}},\quad n\in\mathbb{N}_0,$$ where parameters $a, b, c$, and initial values $x_{-1}$ and $x_0 ...
Stevo Stevic, Bratislav Iricanin, Witold Kosmala, Zdenek Smarda   +3 more
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An explicit solution of third-order difference equations

Journal of Computational and Applied Mathematics, 1994
In this note the author obtains explicit formulas for the solutions of homogeneous and nonhomogeneous third-order difference equations \(y(t + 3) = y(t + 2) + a(t)y(t)\), \(y(i) = c_ i\), \(i = 1,2,3\), respectively, \(y(t + 3) = y(t + 2) + a(t)y(t) + f(t)\), \(y(i) = c_ i\) \(i = 1,2,3\), where \(c_ i\) are constants, \(a(t)\) and \(f(t)\) are ...
openaire   +2 more sources