球面上Yukawa-Beltrami方程的积分方程方法
Integral equation methods for the Yukawa-Beltrami equation on the sphere
AI总结：
本文提出了解决球面多重连通子流形上Yukawa-Beltrami方程的积分方程方法，构建了Yukawa-Beltrami算子的基本解，通过适当表示公式得到紧致积分算子的Fredholm方程，并展示了几组数值例子。
摘要：
本文提出了解决球面多重连通子流形上Yukawa-Beltrami方程的积分方程方法。构建了Yukawa-Beltrami算子的基本解，该基本解可表示为锥函数。利用适当的表示公式，得到一个需要求解的第二类Fredholm方程，其具有紧致积分算子。该积分方程的离散化导致一个条件数与系统规模无关的线性方程组。本文还展示了若干探讨该积分方程性质的数值例子。
英文摘要：
An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Beltrami operator is constructed. This fundamental solution can be represented by conical functions. Using a suitable representation formula, a Fredholm equation of the second kind with a compact integral operator needs to be solved. The discretization of this integral equation leads to a linear system whose condition number is bounded independent of the size of the system. Several numerical examples exploring the properties of this integral equation are presented.
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