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ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER 被引量：3

ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER
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摘要 Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given. Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.
作者 杜金元
机构地区 Department of Mathematics
出处 《Acta Mathematica Scientia》 SCIE CSCD 2004年第1期9-27,共19页 数学物理学报（B辑英文版）
基金 Supported by NNSF and RFDP of Higher Education of China.
关键词 Peano derivative generalized Hermite interpolation singular integral of arbitrary order singular quadrature formula Peano derivative, generalized Hermite interpolation, singular integral of arbitrary order, singular quadrature formula
分类号 O172.2 [理学—基础数学]
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参考文献12

  • 1Kutt H R. The numerical evaluation of principal value integrals by finite-part integration. Numer Math,1975, 24:205-210.
  • 2Kutt H R. On the numerical evaluation of finite-partintegrals involving an algebraic singularity. CSIR Special Report WISK, 1975, 179 (Pretoria).
  • 3Paget D F. The numerical evaluation of Hadamard finte-Dart integrals. Numer Math, 1981, 36:447-453.
  • 4Hunter D B. Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals. Numer Math, 1972, 19:419-424.
  • 5Du Jinyuan. The quadrature formulas for singular integrals of higher order. Chinese Ann of Math, 1985,6A(5): 625-636.
  • 6Du Jinyuan. The quadrature formulas of the closed type and the transformed weight type for singular integrals of higher order. J of Math (PRC),.1986, 6(4): 439-454.
  • 7Du Jinyuan. A note on Riemann boundary value problem of non-normal type. J of Math (PRC), 1990, 10(1): 111-120.
  • 8Lu Jianke. Peano derivatives and singular integrals of arbitrary order. Wuhan University J of Natural Sciences, 1990, 1(1): 9-13.
  • 9Lu Jianke. Boundary Value Problems for Analytic Functions. Singapore: World Scientific, 1993.
  • 10Lu Jianke. Singular integrals of higher order and their applications to the solutions of singular integral equations. SCi & Teeh of Wuhan University,1977, 2:106-122.

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Acta Mathematica Scientia
2004年 第1期

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