@Article{JCM-22-5,
author = {Jin, Huang and Tao, Lü},
title = {The Mechanical Quadrature Methods and Their Extrapolation for Solving BIE of Steklov Eigenvalue Problems},
journal = {Journal of Computational Mathematics},
year = {2004},
volume = {22},
number = {5},
pages = {719--726},
abstract = {<p style="text-align: justify;">By means of the potential theory Steklov eigenvalue problems are transformed into general eigenvalue problems of boundary integral equations (BIE) with the logarithmic singularity. Using the quadrature rules$^{[1]}$, the paper presents quadrature methods for BIE of Steklov eigenvalue problem, which possess high accuracies $O(h^3)$ and low computing complexities. Moreover, an asymptotic expansion of the errors with odd powers is shown. Using $h^3-$Richardson extrapolation, we can not only improve the accuracy order of approximations, but also derive a posterior estimate as adaptive algorithms. The efficiency of the algorithm is illustrated by some examples.</p>},
issn = {1991-7139},
doi = {https://doi.org/2004-JCM-10298},
url = {https://global-sci.com/article/85256/the-mechanical-quadrature-methods-and-their-extrapolation-for-solving-bie-of-steklov-eigenvalue-problems}
}