The Mechanical Quadrature Methods and Their Extrapolation for Solving BIE of Steklov Eigenvalue Problems
Year: 2004
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-10298
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 5 : pp. 719–726
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Steklov eigenvalue problem Boundary integral equation Quadrature method Richardson extrapolation.