Variational method for approximate solution of the Dirichlet problem

Abstract

Abstract. Several numerical methods can be used to approximate the solution of the problem. In order to determine the most effective of them, it is necessary to carefully study each method. The most efficient approximation method is characterized by properties such as high accuracy of the solution, fewer iterations and parameters in the calculation, calculation speed, etc. In this paper we consider the Dirichlet problem for the Poisson equation described by the initial-boundary value problem for the elliptic type of the second order. As an effective iterative method for its approximate solution, variational methods for constructing difference equations and variational methods for constructing iterative algorithms were used. The article presents the results of calculations developed using the variational method for the selected model problem. Examples of calculations for model problems are given. The results of the computational experiment demonstrate the high efficiency of the proposed iterative method.