Volume 22, Issue 5
The Mechanical Quadrature Methods and Their Extrapolation for Solving BIE of Steklov Eigenvalue Problems

J. Comp. Math., 22 (2004), pp. 719-726

Published online: 2004-10

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• Abstract

By means of the potential theory Steklov eigenvalue problems are transformed into general eigenvalue problems of boundary integral equations (BIE) with the logarithmic sin gul arity. Using the quadrature rules['], 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 ap- proximations, but also derive a posterior estimate as adaptive algorithms. The efficiency of the algorithm is illustrated by some examples.

• Keywords

Steklov eigenvalue problem Boundary integral equation Quadrature method Richardson extrapolation

@Article{JCM-22-719, author = {}, 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 = { By means of the potential theory Steklov eigenvalue problems are transformed into general eigenvalue problems of boundary integral equations (BIE) with the logarithmic sin gul arity. Using the quadrature rules['], 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 ap- proximations, but also derive a posterior estimate as adaptive algorithms. The efficiency of the algorithm is illustrated by some examples. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10298.html} }
TY - JOUR T1 - The Mechanical Quadrature Methods and Their Extrapolation for Solving BIE of Steklov Eigenvalue Problems 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 KW - Boundary integral equation KW - Quadrature method KW - Richardson extrapolation AB - By means of the potential theory Steklov eigenvalue problems are transformed into general eigenvalue problems of boundary integral equations (BIE) with the logarithmic sin gul arity. Using the quadrature rules['], 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 ap- proximations, but also derive a posterior estimate as adaptive algorithms. The efficiency of the algorithm is illustrated by some examples.