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- W2022800596 abstract "Algorithms are proposed for the numerical evaluation of Cauchy principal value integrals ⨍−11w(t)f(t)/(t−x)dt, −1<x<1, with weight functions of Jacobi type singularities w(t)=(1−t)α(1+t)β, where α=±1/2 and β=±1/2, for a given function f(t) and Hadamard finite-part integrals ⨎−11w(t)f(t)/(t−x)2dt. The function f is interpolated by using a finite sum of Chebyshev polynomials. The present algorithms require O(NlogN) arithmetic operations, where N is the order of the interpolation polynomial. It is shown that the present scheme gives uniform approximations, namely the errors are bounded independently of x, and is very efficient for smooth f. Further, we discuss approximations of hyper-singular integrals ∫−11w(t)f(t)/(t−x)ndt, n≥3, and show their uniform convergences. Numerical examples are given to demonstrate the performance of the present schemes." @default.
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- W2022800596 date "2011-08-01" @default.
- W2022800596 modified "2023-09-26" @default.
- W2022800596 title "Algorithms for approximating finite Hilbert transform with end-point singularities and its derivatives" @default.
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- W2022800596 doi "https://doi.org/10.1016/j.cam.2011.06.027" @default.
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