Numerical solution of first-order hyperbolic partial differential-difference equation with shift

2010 ◽  
Vol 26 (1) ◽  
pp. 107-116 ◽  
Author(s):  
Paramjeet Singh ◽  
Kapil K. Sharma
Keyword(s):  
Difference Equation ◽  
Numerical Solution ◽  
Partial Differential ◽  
First Order ◽  
Differential Difference Equation

Numerical solution of stochastic partial differential difference equation arising in reliability engineering

2013 ◽  
Vol 219 (14) ◽  
pp. 7645-7652 ◽  
Author(s):  
Manwinder Kaur ◽  
Arvind Kumar Lal ◽  
Satvinder Singh Bhatia ◽  
Akepati Sivarami Reddy
Keyword(s):  
Difference Equation ◽  
Numerical Solution ◽  
Reliability Engineering ◽  
Partial Differential ◽  
Differential Difference Equation

Ladder operators and a differential equation for varying generalized Freud-type orthogonal polynomials

2018 ◽  
Vol 07 (04) ◽  
pp. 1840005 ◽  
Author(s):  
Galina Filipuk ◽  
Juan F. Mañas-Mañas ◽  
Juan J. Moreno-Balcázar
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Inner Product ◽  
Ladder Operators ◽  
First Order ◽  
Standard Family ◽  
Differential Difference Equation ◽  
First Order Differential Equations

In this paper, we introduce varying generalized Freud-type polynomials which are orthogonal with respect to a varying discrete Freud-type inner product. Our main goal is to give ladder operators for this family of polynomials as well as find a second-order differential–difference equation that these polynomials satisfy. To reach this objective, it is necessary to consider the standard Freud orthogonal polynomials and, in the meanwhile, we find new difference relations for the coefficients in the first-order differential equations that this standard family satisfies.

Graphical Solutions for the Characteristic Roots of the First Order Linear Differential-Difference Equation

1979 ◽  
Vol 101 (1) ◽  
pp. 37-43 ◽  
Author(s):  
G. M. Sandquist ◽  
V. C. Rogers
Keyword(s):  
Difference Equation ◽  
Nuclear Reactor ◽  
Mathematical Proof ◽  
Practical Application ◽  
Numerical Accuracy ◽  
Order Linear ◽  
First Order ◽  
Characteristic Roots ◽  
Differential Difference Equation ◽  
Linear Differential

Approximate values for all the apparent real and imaginary characteristic roots of the general first order linear differential-difference equation are determined (primarily graphically) without mathematical proof. These approximate values may then be iterated in a convergent form of the characteristic equation to provide any desired numerical accuracy as shown in several examples. A practical application involving the kinetic behavior of nuclear reactor systems with delayed neutrons is given and compared with the more familiar system solutions.

scholarly journals Zero distribution of polynomials satisfying a differential-difference equation

2014 ◽  
Vol 12 (06) ◽  
pp. 635-666 ◽  
Author(s):  
Diego Dominici ◽  
Walter Van Assche
Keyword(s):  
Difference Equation ◽  
Asymptotic Distribution ◽  
Zeros Of Polynomials ◽  
First Order ◽  
Zero Distribution ◽  
Differential Difference Equation

In this paper, we investigate the asymptotic distribution of the zeros of polynomials Pn(x) satisfying a first-order differential-difference equation. We give several examples of orthogonal and non-orthogonal families.

scholarly journals Results on the solutions of several second order mixed type partial differential difference equations

2021 ◽  
Vol 7 (2) ◽  
pp. 1907-1924
Author(s):  
Wenju Tang ◽  
◽  
Keyu Zhang ◽  
Hongyan Xu ◽  
◽  
...  
Keyword(s):  
Difference Equation ◽  
Finite Order ◽  
Difference Equations ◽  
Mixed Type ◽  
Existence Of Solutions ◽  
Second Order ◽  
Entire Solutions ◽  
Partial Differential ◽  
Differential Difference Equation ◽  
Positive Integers

<abstract><p>This article is concerned with the existence of entire solutions for the following complex second order partial differential-difference equation</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left(\frac{\partial^2 f(z_1, z_2)}{\partial z_1^2}+\frac{\partial^2 f(z_1, z_2)}{\partial z_2^2}\right)^{l}+f(z_1+c_1, z_2+c_2)^{k} = 1, $\end{document} </tex-math></disp-formula></p> <p>where $ c_1, c_2 $ are constants in $ \mathbb{C} $ and $ k, l $ are positive integers. In addition, we also investigate the forms of finite order transcendental entire solutions for several complex second order partial differential-difference equations of Fermat type, and obtain some theorems about the existence and the forms of solutions for the above equations. Meantime, we give some examples to explain the existence of solutions for some theorems in some cases. Our results are some generalizations of the previous theorems given by Qi <sup>[<xref ref-type="bibr" rid="b23">23</xref>]</sup>, Xu and Cao <sup>[<xref ref-type="bibr" rid="b35">35</xref>]</sup>, Liu, Cao and Cao <sup>[<xref ref-type="bibr" rid="b17">17</xref>]</sup>.</p></abstract>

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