• Title, Summary, Keyword: difference-differential equation

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ENTIRE SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATION AND FERMAT TYPE q-DIFFERENCE DIFFERENTIAL EQUATIONS

  • CHEN, MIN FENG;GAO, ZONG SHENG
    • Communications of the Korean Mathematical Society
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    • v.30 no.4
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    • pp.447-456
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    • 2015
  • In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.

A NEW WAY TO FIND THE CONTROLLING FACTOR OF THE SOLUTION TO A DIFFERENCE EQUATION

  • Park, Seh-Ie
    • Journal of the Korean Mathematical Society
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    • v.36 no.5
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    • pp.833-846
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    • 1999
  • In this paper, we will study the relationship between the controlling factor of the solution to a difference equation and the solution of the corresponding differential equation. Many times the controlling factors are the same. But even the controlling factor of the two solutions may be different, we will discover a way to compute, for first order non-linear equations, the controlling factor of the solution to the difference equation using the solution of the differential equation.

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A NOTE ON MEROMORPHIC SOLUTIONS OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS

  • Qi, Xiaoguang;Yang, Lianzhong
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.597-607
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    • 2019
  • In this article, we consider properties of transcendental meromorphic solutions of the complex differential-difference equation $$P_n(z)f^{(n)}(2+{\eta}_n)+{\cdots}+P_1(z)f^{\prime}(z+{\eta}_1)+P_0(z)f(z+{\eta}_0)=0$$, and its non-homogeneous equation. Our results extend earlier results by Liu et al. [9].

The Three-Dimensional Partial Differential Equation with Constant Coefficients of Time-Delay of Alternating Direction Implicit Format

  • Chu, QianQian;Jin, Yuanfeng
    • Journal of Information Processing Systems
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    • v.14 no.5
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    • pp.1068-1074
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    • 2018
  • In this paper, we consider the delay partial differential equation of three dimensions with constant coefficients. We established the alternating direction difference scheme by the standard finite difference method, gave the order of convergence of the format and the expression of the difference scheme truncation errors.

ON ENTIRE SOLUTIONS OF NONLINEAR DIFFERENCE-DIFFERENTIAL EQUATIONS

  • Wang, Songmin;Li, Sheng
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1471-1479
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    • 2013
  • In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form $$f^n+Q(z,f)=h$$, where $n{\geq}2$ is an integer, $Q(z,f)$ is a differential-difference polynomial in $f$ with polynomial coefficients, and $h$ is a meromorphic function of order ${\leq}1$.

A FIFTH ORDER NUMERICAL METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATIONS WITH NEGATIVE SHIFT

  • Chakravarthy, P. Pramod;Phaneendra, K.;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.441-452
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    • 2009
  • In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

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ON PERIODICIZING FUNCTIONS

  • Naito Toshiki;Shin Jong-Son
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.253-263
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    • 2006
  • In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.

A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION

  • KIM, YOUNG-HO;PARK, CHAN-HO;BAE, MUN-JIN
    • Journal of applied mathematics & informatics
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    • v.34 no.5_6
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    • pp.421-434
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    • 2016
  • The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.