TY - JOUR
T1 - The Mechanical Quadrature Methods and Their Extrapolation for Solving BIE of Steklov Eigenvalue Problems
AU - Huang , Jin
AU - Tao , Lü
JO - Journal of Computational Mathematics
VL - 5
SP - 719
EP - 726
PY - 2004
DA - 2004/10
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10298.html
KW - Steklov eigenvalue problem, Boundary integral equation, Quadrature method, Richardson extrapolation.
AB - <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>