In this paper a new modified Nyström method is proposed to solve linear integral equations of the second kind with fixed singularities of Mellin convolution type. It is based on the Gauss–Radau quadrature formula with a suitable Jacobi weight. The stability and convergence of the method is proved in weighted spaces with uniform norm. Moreover, an error estimate of the numerical solution is given under certain assumptions on the Mellin kernel. The efficiency of the method is shown through some examples. The numerical results also confirm that the error estimate is sharp.

中文翻译：

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一致范数加权空间中Mellin积分方程的新稳定数值方法

在本文中，提出了一种新的改进的Nyström方法，以求解具有Mellin卷积型固定奇点的第二类线性积分方程。它基于Gauss-Radau正交公式，具有合适的Jacobi权重。在规范一致的加权空间中证明了该方法的稳定性和收敛性。此外，在梅林内核的某些假设下，给出了数值解的误差估计。通过一些示例显示了该方法的效率。数值结果也证实了误差估计是精确的。