We propose methods for solving an exterior boundary value problem for the Laplace equation based on the main integral Green formula. The main technique is the one of setting an artificial integral boundary condition with iterative improvement. It is shown that iterative methods converge at the rate of a geometric progression. The applicability of the methods for solving exterior problems is confirmed by computational experiments in the two- and three-dimensional cases. The algorithm is also applied to problems with an operator of the mixed type.

中文翻译：

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求解拉普拉斯方程的外边界值问题

我们提出了基于主积分格林公式求解拉普拉斯方程的外边值问题的方法。主要技术是设置人工积分边界条件并迭代改进。结果表明，迭代方法以几何级数的速率收敛。在二维和三维情况下的计算实验证实了解决外部问题的方法的适用性。该算法也适用于混合类型运算符的问题。