Volume 4, Issue 5
The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions

Adv. Appl. Math. Mech., 4 (2012), pp. 603-616.

Published online: 2012-04

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• Abstract

In this paper, the collocation methods are used to solve the boundary integral equations of the first kind on the polygon. By means of Sidi's periodic transformation and domain decomposition, the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers $h_{i}^{3}(i=1,...,d)$, which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations. Numerical experiments are carried out to show that the methods are very efficient.

• Keywords

Splitting extrapolation boundary integral equation of the first kind on polygon collocation method posteriori estimation

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@Article{AAMM-4-603, author = {Li Wang}, title = {The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {5}, pages = {603--616}, abstract = {

In this paper, the collocation methods are used to solve the boundary integral equations of the first kind on the polygon. By means of Sidi's periodic transformation and domain decomposition, the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers $h_{i}^{3}(i=1,...,d)$, which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations. Numerical experiments are carried out to show that the methods are very efficient.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m11159}, url = {http://global-sci.org/intro/article_detail/aamm/138.html} }
TY - JOUR T1 - The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions AU - Li Wang JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 603 EP - 616 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m11159 UR - https://global-sci.org/intro/article_detail/aamm/138.html KW - Splitting extrapolation KW - boundary integral equation of the first kind on polygon KW - collocation method KW - posteriori estimation AB -

In this paper, the collocation methods are used to solve the boundary integral equations of the first kind on the polygon. By means of Sidi's periodic transformation and domain decomposition, the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers $h_{i}^{3}(i=1,...,d)$, which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations. Numerical experiments are carried out to show that the methods are very efficient.

Li Wang. (1970). The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions. Advances in Applied Mathematics and Mechanics. 4 (5). 603-616. doi:10.4208/aamm.10-m11159
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