In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where generalized indicates that a boundary function has a finite number of first kind discontinuity curves. The algorithm consists of the following main stages: (1) the transition from an infinite domain to a finite domain by an inversion; (2) the consideration of a new Dirichlet generalized harmonic problem on the basis of Kelvin theorem for the obtained finite domain; (3) the numerical solution of the new problem for the finite domain by the MPS, which in turn is based on a computer simulation of the Weiner process; (4) finding the probabilistic solution of the posed generalized problem at any fixed points of the infinite domain by the solution of the new problem. For illustration, numerical examples are considered and results are presented.

翻译：本文提出了一种基于概率解法（MPS）的球面外部Dirichlet广义调和问题的数值求解算法，其中“广义”指边界函数具有有限条第一类间断曲线。该算法主要包括以下阶段：（1）通过反演变换将无穷区域转换为有限区域；（2）基于Kelvin定理为所得有限区域建立新的Dirichlet广义调和问题；（3）采用MPS对有限区域的新问题进行数值求解，该方法本身基于Wiener过程的计算机模拟；（4）通过新问题的解求取原广义问题在无穷区域任意给定点处的概率解。文中通过数值算例进行演示并给出计算结果。