Stability theory and adjoint operators for linear differential-difference equations

Linear difference and differential equations

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 ...

Difference integrability conditions for parameterized linear difference and differential equations

This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference isomonodromic with respect to each parameter separately. Due to this result, it is no longer necessary to solve non-linear difference equations to verify isomonodromici...

Linear Operators in the Theory of Partial Differential Equations

Linear Differential Operators for Polynomial Equations

The results of this paper spring from the elementary fact that an algebraic function satisfies a linear differential equation. Let k0 be a number field and k0 be its algebraic closure. Let P ∈ k0(x)[y] be a squarefree polynomial of degree n in y. The derivation δ = d dx extends uniquely to the algebraic closure k0(x) of k0(x). We define the minimal operator associated with P to be the monic dif...