scholarly journals Univariate polynomial solutions of algebraic difference equations

2014 ◽  
Vol 60 ◽  
pp. 15-28 ◽  
Author(s):  
O. Shkaravska ◽  
M. van Eekelen
Keyword(s):  
Difference Equations ◽  
Polynomial Solutions ◽  
Univariate Polynomial ◽  
Algebraic Difference

scholarly journals Asymptotic iteration method for solving Hahn difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lucas MacQuarrie ◽  
Nasser Saad ◽  
Md. Shafiqul Islam
Keyword(s):  
Difference Equations ◽  
Iteration Method ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Asymptotic Iteration Method ◽  
Order Linear ◽  
Polynomial Solutions ◽  
Hahn Difference Equations ◽  
Iteration Methods ◽  
Necessary And Sufficient

AbstractHahn’s difference operator $D_{q;w}f(x) =({f(qx+w)-f(x)})/({(q-1)x+w})$ D q ; w f ( x ) = ( f ( q x + w ) − f ( x ) ) / ( ( q − 1 ) x + w ) , $q\in (0,1)$ q ∈ ( 0 , 1 ) , $w>0$ w > 0 , $x\neq w/(1-q)$ x ≠ w / ( 1 − q ) is used to unify the recently established difference and q-asymptotic iteration methods (DAIM, qAIM). The technique is applied to solve the second-order linear Hahn difference equations. The necessary and sufficient conditions for polynomial solutions are derived and examined for the $(q;w)$ ( q ; w ) -hypergeometric equation.

Polynomial Solutions to the Displacement Analysis of 10-Link 1-DOF Mechanisms

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
A. N. Almadi ◽  
D. Kohli
Keyword(s):  
Closed Form ◽  
Solution Process ◽  
Input Output ◽  
Analysis Problem ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Polynomial Solutions ◽  
Elimination Procedure ◽  
Half Angle ◽  
Univariate Polynomial

Abstract This paper presents closed-form polynomial solutions to the displacement analysis problem of planar 10-link mechanisms with 1 degree-of-freedom (DOF). Using the successive elimination procedure presented herein, the input-output (I/O) polynomials as well as the number of assembly configurations for five mechanisms resulting from two 10-link kinematic chains are presented. It is shown that the displacement analysis problems for all five mechanisms can be reduced to a univariate polynomial devoid of any extraneous roots. This univariate polynomial corresponds to the I/O polynomial of the mechanism. In addition, one of the examples also illustrates how trigonometric manipulations in conjunction with tangent half-angle substitutions can lead to non-trivial extraneous roots in the solution process. Theoretical conditions for identifying and eliminating these extraneous roots are also presented.

scholarly journals Finiteness Properties of Affine Difference Algebraic Groups

2020 ◽  
Author(s):  
Michael Wibmer
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Difference Equations ◽  
General Linear Group ◽  
Algebraic Groups ◽  
The Matrix ◽  
Algebraic Difference ◽  
The Difference ◽  
Linear Differential ◽  
Finiteness Properties

Abstract We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the matrix entries can indeed be defined by finitely many such equations. As an application, we show that the difference ideal of all difference algebraic relations among the solutions of a linear differential equation is finitely generated.

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