Exterior axisymmetric Neumann problem for the Laplace equation: Numerical algorithms without saturation

The development of the numerical solution of an external axisymmetric Neumann problem for the Laplace equation, is discussed. The numerical method is established by computing the nonseparated axisymmetric potential flow of an inviscid incompressible fluid that past an ellipsoid with an aspect ratio of 1000. The achievements in the theory of constructive function approximation on the interval help the achieve accurate solution problem. The method solves the problem in the form of a single-layer potential with a density that is invariant with the axis. An unsaturated discretization of integral equation is derived for approximate the solution. The approximation method, which involves linear algebra procedures, for determining the accuracy of the constructed numerical solution. The logarithmic singularity is represented as a factor in the method. The method also implements verified computations for accurate solution.