SOLUTION OF THE DIRICHLET PROBLEM FOR LAPLACE'S EQUATION ON A CIRCLE

This work considers the solution of the Dirichlet problem for the Laplace equation in the case when the domain is bounded by a circle. The Laplace equation and its basic properties are introduced, and the transition to polar coordinates is carried out. The formulation of the Dirichlet problem on a circle with given boundary conditions is presented. The method of solving this problem using trigonometric series and the Fourier series to satisfy the boundary conditions is described. Specific examples of solving the Dirichlet problem on a circle with illustrations and numerical results are provided. In conclusion, the importance and practical significance of the obtained solutions for various applied problems are emphasized.