scholarly journals Some families of differential equations associated with the Gould-Hopper-Frobenius-Genocchi polynomials

2021 ◽  
Vol 7 (3) ◽  
pp. 4851-4860
Author(s):  
Rabab Alyusof ◽  
◽  
Mdi Begum Jeelani ◽  
Keyword(s):  
Differential Equations ◽  
Recurrence Relation ◽  
Partial Differential ◽  
Shift Operators ◽  
Genocchi Polynomials ◽  
Factorization Technique ◽  
Basic Objective

<abstract><p>The basic objective of this paper is to utilize the factorization technique method to derive several properties such as, shift operators, recurrence relation, differential, integro-differential, partial differential expressions for Gould-Hopper-Frobenius-Genocchi polynomials, which can be utilized to tackle some new issues in different areas of science and innovation.</p></abstract>

scholarly journals Some families of differential equations associated with the Hermite-based Appell polynomials and other classes of Hermite-based polynomials

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 695-708 ◽  
Author(s):  
H.M. Srivastava ◽  
M.A. Özarslan ◽  
Banu Yılmaz
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Bernoulli Polynomials ◽  
Factorization Method ◽  
Euler Polynomials ◽  
Appell Polynomials ◽  
Partial Differential ◽  
Genocchi Polynomials

Recently, Khan et al. [S. Khan, G. Yasmin, R. Khan and N. A. M. Hassan, Hermite-based Appell polynomials: Properties and Applications, J. Math. Anal. Appl. 351 (2009), 756-764] defined the Hermite-based Appell polynomials by G(x, y, z, t) := A(t)?exp(xt + yt2 + zt3) = ??,n=0 HAn(x, y, z) tn/n! and investigated their many interesting properties and characteristics by using operational techniques combined with the principle of monomiality. Here, in this paper, we find the differential, integro-differential and partial differential equations for the Hermite-based Appell polynomials via the factorization method. Furthermore, we derive the corresponding equations for the Hermite-based Bernoulli polynomials and the Hermite-based Euler polynomials. We also indicate how to deduce the corresponding results for the Hermite-based Genocchi polynomials from those involving the Hermite-based Euler polynomials.

scholarly journals On the numerical solution of the diffusion equation with a nonlocal boundary condition

2003 ◽  
Vol 2003 (2) ◽  
pp. 81-92 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Differential Equations ◽  
Diffusion Equation ◽  
Recurrence Relation ◽  
Exponential Function ◽  
Nonlocal Boundary ◽  
Matrix Exponential ◽  
Finite Difference Approximation ◽  
Partial Differential ◽  
First Order ◽  
Matrix Exponential Function

Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (MOL) semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations (ODEs). The partial derivative with respect to the space variable is approximated by a second-order finite-difference approximation. The solution of the resulting system of first-order ODEs satisfies a recurrence relation which involves a matrix exponential function. Numerical techniques are developed by approximating the exponential matrix function in this recurrence relation. We use a partial fraction expansion to compute the matrix exponential function via Pade approximations, which is particularly useful in parallel processing. The algorithm is tested on a model problem from the literature.

scholarly journals Differential and integral equations for Legendre-Laguerre based hybrid polynomials

2021 ◽  
Vol 73 (3) ◽  
pp. 408-421
Author(s):  
S. Khan ◽  
M. Riyasat ◽  
Sh. A. Wani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Equations ◽  
Recurrence Relations ◽  
Volterra Integral Equations ◽  
Series Expansions ◽  
Appell Polynomials ◽  
Shift Operators ◽  
Genocchi Polynomials ◽  
Differential And Integral Equations

UDC 517.9 In this article, a hybrid family of three-variable Legendre – Laguerre – Appell polynomials is explored and their properties including the series expansions, determinant forms, recurrence relations, shift operators, followed by differential, integro-differential and partial differential equations are established. The analogous results for the three-variable Hermite – Laguerre – Appell polynomials are deduced. Certain examples in terms of Legendre – Laguerre – Bernoulli, –E uler and – Genocchi polynomials are constructed to show the applications of main results. A further investigation is performed by deriving homogeneous Volterra integral equations for these polynomials and for their relatives.

On some classes of differential equations and associated integral equations for the Laguerre–Appell polynomials

2018 ◽  
Vol 9 (3) ◽  
pp. 185-194 ◽  
Author(s):  
Subuhi Khan ◽  
Mumtaz Riyasat ◽  
Shahid Ahmad Wani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Equations ◽  
Recurrence Relations ◽  
Laguerre Polynomials ◽  
Factorization Method ◽  
Volterra Integral Equations ◽  
Appell Polynomials ◽  
Partial Differential ◽  
Genocchi Polynomials

Abstract The article aims to explore some new classes of differential equations and associated integral equations for some hybrid families of Laguerre polynomials. The recurrence relations and differential, integro-differential and partial differential equations for the hybrid Laguerre–Appell polynomials are derived via the factorization method. An analogous study of these results for the hybrid Laguerre–Bernoulli, Euler and Genocchi polynomials is presented. Further, the Volterra integral equations for the hybrid Laguerre–Appell polynomials and for their corresponding members are also explored.

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

Partial Differential Equations in Fluid Dynamics

2008 ◽  
Author(s):  
Isom H. Herron ◽  
Michael R. Foster
Keyword(s):  
Fluid Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

Dispersive Partial Differential Equations

2016 ◽  
Author(s):  
M. Burak Erdogan ◽  
Nikolaos Tzirakis
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential
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