We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.

For the analysis of multi-grid methods applied to finite difference discretizations, two definitions of orders of intergrid transfer operators are being used. The order is either defined in terms of the symbol of the transfer operator, i.e., its Fourier transform, or as the order of polynomials being preserved. In [J. Comput. Appl. Math., 32(3) (1990), pp. 423–429], Hemker showed that the secon...

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...