### EXTRAPOLATION METHODS FOR COMPUTING HADAMARD FINITE-PART INTEGRAL ON FINITE INTERVALS

Jin Li1, Hongxing Rui2

1. 1. School of Science, Shandong Jianzhu University, Jinan 250101, China;
2. School of Mathematics, Shandong University, Jinan 250100, China
• Received:2017-02-16 Revised:2017-10-09 Online:2019-03-15 Published:2019-03-15
• Supported by:

The work of Jin Li was supported by National Natural Science Foundation of China (Grant No. 11471195, Grant No.11771398 and Grant No.91330106), China Postdoctoral Science Foundation (Grant No. 2015T80703) and Shandong Provincial Natural Science Foundation of China (Grant No. ZR2016JL006).

Jin Li, Hongxing Rui. EXTRAPOLATION METHODS FOR COMPUTING HADAMARD FINITE-PART INTEGRAL ON FINITE INTERVALS[J]. Journal of Computational Mathematics, 2019, 37(2): 261-277.

In this paper, we present the composite rectangle rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel 1/(x-s)2 and we obtain the asymptotic expansion of error function of the middle rectangle rule. Based on the asymptotic expansion, two extrapolation algorithms are presented and their convergence rates are proved, which are the same as the Euler-Maclaurin expansions of classical middle rectangle rule approximations. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.

CLC Number:

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