Choosing of optimal start approximation for laplace equation numerically solving

Abstract

In the last few years, repeatedly increased the role of simulation systems for solution of physical problems, particularly in the microwave and electronics. This article focuses on the promising methods for setting an initial approximation for the numerical solution of the Laplace equation. We investigate Dirichlet problem for a case of two-dimensional area with lime border, numerical scheme for solving this equation is widely knowns it finite difference method. One of the major stages in the algorithm for that numerical solution is choosing of start approximation, usually as the initial values of the unknown function are assumed to be zero, which may serve as a lead to a large number of iterations in finding the numerical solution. It is shown that there is a way to set a start approximation, which can significantly reduce the number of iterations in the solution of the Laplace equation.

Keywords: Laplace equation; approximation; net; Dirichlet problem; finite difference
method.