Applied mathematics

Properties of finite-difference analog of one-dimensional Laplace operator on the graph

O. A. Makhinova

Voronezh State University

Abstract: The finite-difference analogs of one-dimensional Laplace operator on the graph-star and the graph with a cycle are considered. At the same time differential operator characteristic continuity at its reduction to the finite-difference analog is essential: the structure of an eigenvalue set is similar to the structure of a proper value set of a differential operator, completeness of eigenvectors in the finite-dimensional space remains, the finite-difference analog of Laplace operator remains symmetric and positive.

Keywords: one-dimensional Laplace operator, finite-difference analog of Laplace operator, characteristics of operator.

UDC: 517.95


Accepted: October 20, 2011