Abstract
An automatic integration scheme is presented for evaluating the indefinite integral of function with a logarithmic singularity \( I(x,y,c) - \int\limits_x^y f (t)1n|t - c|dt \), a ≤ x, y, c ≤ b, within a finite range [a, b] for some smooth functions f(t), whose Chebyshev series expansions over [a, b] are of rapid convergence. The Fast Fourier Transform (FFT) and recurrence relations are made use of to compute the Chebyshev coefficients of f(t) and to expand the indefinite integral I(x, y, c) in the Chebyshev series by using auxiliary logarithmic functions. Numerical examples illustrating the performance of the present method are given.
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© 1988 Springer Basel AG
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Hasegawa, T., Torii, T. (1988). Indefinite Integration of Function Involving Logarithmic Singularity by the Chebyshev Expansion. In: Agarwal, R.P., Chow, Y.M., Wilson, S.J. (eds) Numerical Mathematics Singapore 1988. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 86. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6303-2_16
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DOI: https://doi.org/10.1007/978-3-0348-6303-2_16
Publisher Name: Birkhäuser, Basel
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