Field calculation of the open magnetic systems by the regularization of Cauchy problem

The calculation of the scalar magnetic potential distribution of the open electromagnetic systems called a Cauchy problem for the Laplace equation consists in the solution of equation /spl Delta/U=0 under the given boundary conditions, where /spl Delta/ is a differential Laplacian operator. This problem is not correct in the Adamar sense because its solution has no stability. A quasi-transformation method was used for the field solution. It consists in the variation of the differential operators of the Laplacian equation. This variation is carried out introducing the additional differential terms. As a result, an incorrect problem is replaced with a family of correct problems. The further solution has been realized by a numerical finite difference method.