On the Correctness of Polynomial Difference Operators

Abstract

The correctness Cauchy problem is explored for a polynomial difference operator. The easily verifiable sufficient condition correctness for the Cauchy problem for a polynomial difference operator with constant coefficients is proved whose characteristic polynomial is homogeneous.

Correctness of a Two-dimensional Cauchy Problem for a Polynomial Difference Operator with Constant Coefficients

“…In [13] we have studied solvability of difference equations with initial-boundary Riquiertype conditions; in terms of the theory of difference schemes they are multilayer implicit difference schemes. In [14] an easily verifiable sufficient condition for correctness of a Cauchy problem for a polynomial difference operator with constant coefficients whose characteristic polynomial is homogeneous has been obtained.…”