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Numerical evaluation of integrals of periodic functions with Cauchy and Poisson type kernels

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Summary

We modify the trapezoidal sequence of rules to obtain quadrature formulas for the numerical evaluation of integrals of periodic functions with Cauchy and Poisson type kernels. Our modified quadrature formulas give much better approximate values for these integrals than the trapezoidal rule; numerical examples are given for comparison.

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References

  1. Davis, P. J.: On the numerical integration of periodic analytic functions. On numerical approximation (R. E. Langer, ed.), pp. 45–59, Madison: University of Wisconsin Math. Research Center, 1959.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Hauz Khas, 29, New Delhi, India

    M. M. Chawla & T. R. Ramakrishnan

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  1. M. M. Chawla
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  2. T. R. Ramakrishnan
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Chawla, M.M., Ramakrishnan, T.R. Numerical evaluation of integrals of periodic functions with Cauchy and Poisson type kernels. Numer. Math. 22, 317–323 (1974). https://doi.org/10.1007/BF01406970

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  • DOI: https://doi.org/10.1007/BF01406970

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