Descent for differential Galois theory of difference equations: confluence andq-dependence

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 ...

Galois theory of fuchsian q-difference equations

We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff’s classification scheme with the connection matrix to define and describe their Galois groups. Then we describe fundamental subgroups that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger’s type.

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Galois Theory of Linear Differential Equations

Galois Theory of Linear Differential Equations - ReadingSample