TY - JOUR
TI - Nystrom methods and combination for solving the first-kind boundary integral equation
AU - Li Yong-Zheng
AU - Huang Le-Ming
AU - Zheng Ke-Long
JN - Thermal Science
PY - 2024
VL - 28
IS - 4
SP - 3573
EP - 3579
PT - Article
AB - Based on the single-layer potential theory, the Laplace equation can be  converted into the problem of the first-kind boundary integral equation  (BIE1st). The kernel of BIE1st is characterized by the logarithmic  singularity. In this paper, we investigate the Nystrom method for solving  the BIE1st. The numerical solutions possess high accuracy orders O(h3) and  the combination of two kinds of Nystrom solutions has the same accuracy as  the result with double grid. Furthermore, by the double power  transformation, the proposed method can be used to deal with the problem on  the non-smooth boundary and has the higher accuracy. The efficiency is  illustrated by some examples.