科研之友
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摘要
This article presents approximations of the hypersingular integrals integral(b)(a) g(x)(x - t)(alpha)dx and integral(b)(a) g(x)vertical bar x - t vertical bar(alpha)dx with arbitrary singular point t is an element of (a, b) and negative fraction number alpha < -1. These general expansions are applicable to a large range of hypersingular integrals, including both popular hypersingular integrals discussed in the literature and other important ones which have not been addressed yet. The corresponding mid-rectangular formulas and extrapolations, which can be calculated in fairly straightforward ways, are investigated. Numerical examples are provided to illustrate the features of the numerical methods and verify the theoretical conclusions.
- 出版日期2018
- 单位四川大学
