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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 12 | Number 1 | Year 2014 | Article Id. IJMTT-V12P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V12P504

Numerical Evaluation of Integrals of Analytic Functions


B. P. Acharya, M. Acharya, S. B. Sahoo
Abstract

Some quadrature rules involving values of the integrand and its derivatives at a certain set of nodes in the domain of analyticity of an analytic function have been constructed for the numerical evaluation of the contour integral of the function along a directed line segment. The degree of precision of the quadrature rules has been enhanced by examining the truncation error associated with the quadrature rules.

Keywords
Analytic functions, Quadrature rules, Degree of precision
References

[1] G. Birkhoff and D. M. Young, “Numerical quadrature of analytic and harmonic functions”, J. Math. Phys., Vol. 29, pp. 217 – 221, 1950.
[2] D. D. Tosic, “A modification of the Birkhoff-Young quadrature formula for analytic functions”, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 602 – 633, pp.170-172, 1978.
[3] F. G. Lether, “On Birkhoff-Young quadrature of analytic functions “, J. Copm. Appl. Math., Vol. 2, pp.81 – 84, 1976.
[4] M. Acharya, B. P. Acharya and M. M. Nayak, “Approximate evaluation of integrals of analytic functions”, FACTA Universitatis (NIS) Ser. Math. Inform., Vol. 23, pp.63-68, 2008.
[5] G. V. Milovanovic, “Generalized quadrature formulae for analytic functions”, Appl. Math. & computation, Vol. 218, pp.8537 – 8551, 2012.

Citation :

B. P. Acharya, M. Acharya, S. B. Sahoo, "Numerical Evaluation of Integrals of Analytic Functions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 1, pp. 27-30, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V12P504

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