NYSTROM METHODS AND COMBINATION FOR SOLVING THE FIRST-KIND BOUNDARY INTEGRAL EQUATION.

Based on the single-layer potential theory, the Laplace equation can be converted into the problem of the first-kind boundary integral equation (BIE^1st). The kernel of BIE^1st is characterized by the logarithmic singularity. In this paper, we investigate the Nystrom method for solving the BIE^1st. 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. [ABSTRACT FROM AUTHOR]