Numerical implementation of nonstationary axisymmetric problems of an ideal incompressible fluid with free surface

A fundamentally new unsaturated technique for the numerical solution of the Dirichlet–Neumann problem for the Laplace equation was designed. This technique makes it possible, due to the smoothness of the sought solution of the problem, to take into account the axisymmetric specificity of the problem, which prevents the use of any saturated numerical methods, i. e., methods with a leading error term.