کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645756 | 1342061 | 2009 | 15 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs](/preview/png/4645756.png)
This paper presents the mechanical quadrature methods (MQMs) for solving boundary integral equations (BIEs) of the first kind on open arcs. The spectral condition number of MQMs is only O(h−1), where h is the maximal mesh width. The errors of MQMs have multivariate asymptotic expansions, accompanied with for all mesh widths hi. Hence, once discrete equations with coarse meshes are solved in parallel, the accuracy order of numerical approximations can be greatly improved by splitting extrapolation algorithms (SEAs). Moreover, a posteriori asymptotic error estimates are derived, which can be used to formulate self-adaptive algorithms. Numerical examples are also provided to support our algorithms and analysis. Furthermore, compared with the existing algorithms, such as Galerkin and collocation methods, the accuracy order of the MQMs is higher, and the discrete matrix entries are explicit, to prove that the MQMs in this paper are more promising and beneficial to practical applications.
Journal: Applied Numerical Mathematics - Volume 59, Issue 12, December 2009, Pages 2908-2922