The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval | Zendy

Jin Li | Zendy; Xiuzhen Li | Zendy

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The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval

Author(s) -

Jin Li,

Xiuzhen Li

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/736834

Subject(s) - mathematics , quadrature (astronomy) , computation , a priori and a posteriori , rate of convergence , trapezoidal rule , function (biology) , taylor series , interval (graph theory) , convergence (economics) , boundary (topology) , asymptotic expansion , order (exchange) , numerical integration , mathematical analysis , algorithm , computer science , combinatorics , channel (broadcasting) , computer network , philosophy , epistemology , finance , evolutionary biology , economic growth , electrical engineering , economics , biology , engineering

The modified trapezoidal rule for the computation of hypersingular integrals in boundary element methods is discussed. When the special function of the error functional equals zero, the convergence rate is one order higher than the general case. A new quadrature rule is presented and the asymptotic expansion of error function is obtained. Based on the error expansion, not only do we obtain a high order of accuracy, but also a posteriori error estimate is conveniently derived. Some numerical results are also reported to confirm the theoretical results and show the efficiency of the algorithms

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