An Algorithm Determining the Difference Galois Group of Second Order Linear Difference Equations

An Algorithm Determining the Difference Galois Group of Second Order Linear Difference Equations

groups are the groups Dk,l,e = {( α 0 0 δ ) ∈ D | α = 1, δ = 1, ααδδ = 1 } with l, k, e ∈ Z≥1 and gcd(k, l, e) = 1, where gα = k gcd(k,l) and gδ = l gcd(k,l) . If G is a one-dimensional algebraic subgroup of D then G is equal to a group Dm,n = {( α 0 0 δ ) ∈ D | αδ = 1 } with m,n ∈ Z. For all m,n ∈ Z we have that Dm,n/D m,n

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

σ-Galois theory of linear difference equations

Inspired by the numerous applications of the differential algebraic independence results from [36], we develop a Galois theory with an action of an endomorphism σ for systems of linear difference equations of the form φ(y) = Ay , where A ∈ GLn(K ) and K is a φσ-field, that is, a field with two given commuting endomorphisms φ and σ, like in Example 2.1. This provides a technique to test whether ...

An Algorithm for Nondominant Solutions of Linear Second-order Inhomogeneous Difference Equations

An algorithm is given for computing a weighted sum of a nondominant solution of a linear second-order inhomogeneous difference equation to a prescribed accuracy by estimating the truncation error. The present method is an extension of both the stable numerical method due to Olver and Sookne and a summation technique due to Deuflhard for computing minimal solutions of a homogeneous difference eq...

On Lie Group Classification of Second{order Ordinary Difference Equations