The artificial boundary conditions replacing the difference approximation of Beltrami equation on a sphere outside the artificially restricted computational domains are constructed in this paper by means of difference potentials method. The introducing of the small parameter allows to use an easy auxiliary problem which can be solved by method of variables separation. As the small parameter tends to zero, the matrix of the obtained boundary conditions converges to the matrix of the accurate artificial boundary conditions (constructed without using of the small parameter). The first order of the convergence is proved. Some results of computations are presented.

Mathematical problems and theory of numerical methods

Mishkov M. N.,  KIAM RAS