## Taiwanese Journal of Mathematics

### SPLITTING EXTRAPOLATIONS FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF MIXED BOUNDARY CONDITIONS ON POLYGONS BY MECHANICAL QUADRATURE METHODS

#### Abstract

To solve the boundary integral equations (BIE) of mixed boundary conditions, we propose the mechanical quadrature methods (MQM) using specific quadrature rule to deal with weakly singular integrals. Denote $h_{m}$ as the mesh width of a curved edge $\Gamma_{m}$ ($m=1,...,d)$ of polygons. Then the multivariate asymptotic expansions of solution errors are found to be $O(h^{3}),$ where $h=\max_{1\leq m\leq d}h_{m}.$ Hence, by using the splitting extrapolation methods (SEM), the high convergence rates as $O(h^{5})$ can be achieved. Moreover, numerical examples are provided to support our theoretical analysis.

#### Article information

Source
Taiwanese J. Math., Volume 12, Number 9 (2008), 2341-2361.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405183

Digital Object Identifier
doi:10.11650/twjm/1500405183

Mathematical Reviews number (MathSciNet)
MR2479059

Zentralblatt MATH identifier
1176.65142

Subjects
Primary: 65R20: Integral equations 45L10

#### Citation

Huang, Jin; Li, Zi Cai; L¨u, Tao; Zhu, Rui. SPLITTING EXTRAPOLATIONS FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF MIXED BOUNDARY CONDITIONS ON POLYGONS BY MECHANICAL QUADRATURE METHODS. Taiwanese J. Math. 12 (2008), no. 9, 2341--2361. doi:10.11650/twjm/1500405183. https://projecteuclid.org/euclid.twjm/1500405183

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