THE METHOD OF FICTITIOUS DOMAINS FOR THE LAPLACE EQUATION WITH HETEROGENEOUS BOUNDARY-CONDITIONS

The method of fictitious domains is used for the numerical solution of the Laplace equation with inhomogeneous boundary conditions of the first kind in a region with time-dependent boundary. Implicit and modified alternate-triangular iterative methods with Chebyshev parameters are considered. The operators of the methods are chosen from the condition that the rate of convergence of iterations is independent of the small parameter of the method of fictitious domains. The results of numerical calculations are described and compared with the analytic solution of the problem.