This paper investigate on numerical analysis on modified Single-layer approach to exterior Dirichlet problem of Laplace equation. We complete the convergence and error analysis of Petrov-Galerkin and Galerkin-Collocation methods with trigonometric basis for the induced modified Symm's integral equation of the first kind on analytic boundary. Besides, utilizing the composite trapezial quadrature formula and trigonometric interpolation to handle the singularity in modified logarithmic kernel, we establish the numerical procedure for implementation. On these numerical examples, we compare the effect and efficiency of different Petrov-Galerkin and Galerkin-Collocation methods.

中文翻译：

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拉普拉斯方程外Dirichlet问题的边界积分方程数值分析

本文研究了Laplace方程外Dirichlet问题的修正单层方法的数值分析。针对解析边界上的第一类诱导修正Symm积分方程，我们用三角函数完成了Petrov-Galerkin和Galerkin-Collocation方法的收敛性和误差分析。此外，利用复合梯形求积公式和三角插值处理修正对数核中的奇异性，我们建立了实现的数值程序。在这些数值例子中，我们比较了不同的 Petrov-Galerkin 和 Galerkin-Collocation 方法的效果和效率。