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

Jin Huang & Lü Tao

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 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.

  • Keywords

Steklov eigenvalue problem, Boundary integral equation, Quadrature method, Richardson extrapolation.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-719, author = {Huang , Jin 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 = {

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.

}, 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 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 -

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.

Huang , Jin and Tao , Lü. (2004). The Mechanical Quadrature Methods and Their Extrapolation for Solving BIE of Steklov Eigenvalue Problems. Journal of Computational Mathematics. 22 (5). 719-726. doi:
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