Abstract Estimates of stability in the sense perturbation of the operator for
solving first- and second-order differential-operator equations have been obtained. For
two- and three-level operator-difference schemes with weights similar estimates hold.
Using the results obtained, we construct estimates of the coefficient stability for onedimensional
parabolic and hyperbolic equations as well as for the difference schemes
approximating the corresponding differential problems.
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.
Consistent systems of linear differential and difference equations
