TY - JOUR
T1 - The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions
AU - Wang , Li
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, boundary integral equation of the first kind on polygon, collocation method, posteriori estimation.
AB - <p style="text-align: justify;">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&#39;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.</p>