Об оптимальных итерационных и прямых методах решения задачи Дирихле для уравнения Пуассона

For the numerical solution of the Dirichlet problem for the Poisson equation, both direct and iterative methods have been developed. However, the required number of arithmetic operations for direct methods, as well as the number of iterations in iterative methods, often turns out to be very large. For this reason, the issues of high accuracy and efficiency of various methods remain relevant. In this work, a new high-accuracy and efficient method is proposed for the numerical solution of the Dirichlet problem for the Poisson equation – a discrete version of the preliminary integration method, which significantly surpasses existing direct and iterative methods in terms of the number of arithmetic operations. The efficiency of the proposed method is illustrated by tabular and graphical results.