A mixed quadrature rule of modified Birkhoff-Young rule and SM2(f) rule for the numerical integration of analytic functions ∗

Sanjit Kumar Mohanty

doi:10.48165/

Authors

Sanjit Kumar Mohanty Department of Mathematics, B.S. College, Nuahat, Jajpur, Odisha 754024, India.

DOI:

https://doi.org/10.48165/

Keywords:

Quadrature rule, Asymptotic error, Analytic function, Numerical in tegration, Modified Birkhoff-Young rule, Richardson Extrapolation, SM2 (f), SM6 (f), ESM2, ESM6

Abstract

A quadrature rule of higher precision is constructed in this paper by mixing two quadrature rules of lower precision for an approximate evaluation of the integral of an analytic function over a line segment in the complex plane. An asymptotic error estimate of the rule is also determined and the rule is numerically verified.

References

Das, R.N. and Pradhan, G. (1997) A mixed quadrature rule for numerical integration of analytic functions, Bull. Cal. Math. Soc, 89, 37–42.

Acharya, B.P. and Das, R.N. (1983). Compound Birkhoff-Young rule for numerical integration of analytic functions, Int. J. Math. Educ. Sci. Technol., 14(1), 101–109.

Birkhoff, G. and Young, D. (1950). Numerical quadrature of analytic and harmonic functions, J. Math. Phys., 29, 217–227.

Das, R.N and Pradhan, G. 1996. A mixed quadrature rule for approximate evaluation of real definite integrals, Int. J. Math. Educ. Sci. Techonol., 27(2), 279–283.

Mohanty, Sanjit K. and Dash, R.B. (2011). A mixed quadrature rule for numerical integration of analytic functions using Birkhoff-Young and Bool’s quadrature system, News Bull. Cal. Math. Soc., 34(1–3), 17–20.

Mohanty, Sanjit K. and Dash, R.B. (2008). A mixed quadrature rule for numerical ntegration of analytic functions, Bulletin of Pure and Applied Sciences Section E Math and Stat., 27E(2), 373–376.

Lether, F.G. (1976). On Birkhoff-Young quadrature of analytic function, J. Comput. Appl. Math., 2, 81–92.

Dash, R.B and Jena, Saumya Ranjan (2008). A mixed quadrature of Birkhoff-Young using Richard son extrapolation and Gauss-Legendre 4 point transformed rule, Int. J. Appl. Math and Applica tion, 1(2), 111–117.