Superconvergence of Hermite rule for hypersingular integrals on interval

Abstract

In this paper, the composite Hermite rule for the computation of the hypersingular integrals on interval is studied and the error expansion is presented. The superconvergence result of the Hermite rule is derived, which is one order higher than general. At last, several numerical examples are provided to validate the theoretical analysis.

Keywords:

• hypersingular integral
• boundary elment methods
• composite Hermite rule
• superconvergence
• error expansion

2000 AMS Subject Classifications:

• 65D30
• 65D32

Acknowledgements

The first and third authors are supported by the NNSF of China (Nos. 11101247, 11101246 and 11201209) and the NSF of Shandong Province (ZR2011AQ020). The second author is supported by the NNSF of China (No. 11171190).