Spline galerkin methods for the sherman-lauricella equation on contours with corners

Didenko, Victor D.1; Tang, Tao2,3; Vu, Anh My1

2015

10.1137/140997968

SIAM JOURNAL ON NUMERICAL ANALYSIS   影响因子和分区

0036-1429

Spline Galerkin approximation methods for the Sherman-Lauricella integral equation on simple closed piecewise smooth contours are studied, and necessary and sufficient conditions for their stability are obtained. It is shown that the method under consideration is stable if and only if certain operators associated with the corner points of the contour are invertible. Numerical experiments demonstrate a good convergence of the spline Galerkin methods and validate theoretical results. Moreover, it is shown that if all corners of the contour have opening angles located in interval (0.1, 1.9), then the corresponding Galerkin method based on splines of order 0, 1, or 2 is always stable. These results are in strong contrast with the behavior of the Nystrom method, which has a number of instability angles in the interval mentioned.
© 2015 Society for Industrial and Applied Mathematics.

EI ; SCI

其他

WOS:000367019800013

Society for Industrial and Applied Mathematics Publications

20162402484310

Convergence of numerical methods ; Integral equations

Calculus:921.2 ; Numerical Methods:921.6

MATHEMATICS

EV Compendex

1.Faculty of Science, Universiti Brunei Darussalam, Bandar Seri Begawan; BE1410, Brunei
2.Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
3.Department of Mathematics, South University of Science and Technology, Shenzhen, Guangdong; 518055, China

Didenko, Victor D.,Tang, Tao,Vu, Anh My. Spline galerkin methods for the sherman-lauricella equation on contours with corners[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2015,53(6):2752-2770.

Didenko, Victor D.,Tang, Tao,&Vu, Anh My.(2015).Spline galerkin methods for the sherman-lauricella equation on contours with corners.SIAM JOURNAL ON NUMERICAL ANALYSIS,53(6),2752-2770.

Didenko, Victor D.,et al."Spline galerkin methods for the sherman-lauricella equation on contours with corners".SIAM JOURNAL ON NUMERICAL ANALYSIS 53.6(2015):2752-2770.