Solvability of the Cauchy Problem with a Polynomial Difference Operator

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

“…In the case of a purely implicit scheme, namely when σ 1 = 1, σ 2 = 0, Θ = 3 2 , the scheme (12) can be written as …”

“…A difference analog of the boundary value problem of Hörmander for a polynomial differential operator has been studied in [12] in two-dimensional case and in [13] for arbitrary number of variables. 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.…”

On the Correctness of Polynomial Difference Operators

“…[10,12,13]). (6) is a solution of P β (x) to the equation P (δ)P β (x) = δ 0 (x) satisfying the initial conditions P β (x) = 0 for x ∈ X 0,β where…”