On some possible applications of Laplace operator in a revolved coordinate system for numerical calculations

Abstract

The Laplace operator in a revolved coordinate system (the “revolved” Laplace operator) is introduced in numerical mesh method along diagonal lines. In this paper an attempt is made to use it for numerical solution of the two-dimensional Poisson equation. Advantages and disadvantages of this approach and difficulties in its realization are discussed.

Keywords

• poisson equation, finite-difference method, boundary value problem, ‘revolved’ laplace operator, method of transition to a steady state.