In this paper, the collocation method is applied on two-dimensional integral equations of the second kind on non-rectangular domains. Since the domains of these equations are non-rectangular and so directly applying the collocation method for them is difficult, at first, the integral equations are converted to equivalent integral equations on rectangular domains. Then, two-dimensional Jacobi collocation method is applied. Furthermore, an error estimate for the method is investigated and several examples demonstrate the accuracy and efficiency of the method.

中文翻译：

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用误差估计求解非矩形域上的第二类二维积分方程

本文将搭配方法应用于非矩形域上的第二类二维积分方程。由于这些方程的域是非矩形域，直接对它们应用搭配方法比较困难，首先将积分方程转化为矩形域上的等效积分方程。然后，应用二维雅可比搭配方法。此外，研究了该方法的误差估计，并且几个例子证明了该方法的准确性和效率。