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Application of two mixed Quadrature rules using an anti-Gaussian Quadrature rule in the Adaptive quadrature routine

Bibhu Prasad Singh, Dr. Rajani Ballav Dash

Abstract


A model is set up which embodies the basic features of Adaptive quadrature routines
involving mixed rules. Not before mixed quadrature rules basing on anti-Gaussian quadrature rule have been used for fixing termination criterionin Adaptive quadrature routines. Two mixed quadrature rules of higher precision for approximate evaluation of real definite integrals have been constructed using an anti-Gaussian rule for this purpose. The first is linear combination of anti-Gaussian three point rule and Fejers three point first rule, the second is the linear combination of anti-Gaussian three point rule and Fejers three point second rule.The analytical convergence of the rules have been studied. The error bounds have been determined asymptotically. Adaptive quadrature routines being recursive by nature, a termination criterion is formed taking in to account two mixed quadrature rules. The algorithm presented in this paper has been “C” programmed and successfully tested on different integrals. The efficiency of the process is reflected in the table at the end.


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References


Dirk P. Laurie., Anti-Gaussian quadrature formulas, mathematics of computation, Vol. 65, Number : 214, April 1996 pages 739-749.

Conte .S. and Boor,C.D., Elementary Numerical Analysis, Mc-Graw Hill,(1980).

Abromowitz , M . and Stegun, A., Iren: Handbook of Mathematical Functions, Dover Publication Inc., New York,(1965). [4] Davis, J.P. and P. Rabinowitz , P., Methods of numerical integration ,2nd ed. Academic press Inc. san Diego,(1984).

Das, R.N. and Pradhan , G., A mixed quadrature rule for approximate evaluation of real Definite Integrals, Int. J. math. Educ. Sci. Technol., 27(2) (1996),279 - 283.

Dash, R.B. and Das, D., A mixed quadrature rule by blending Clenshaw- Curtis and Gauss-Legendre quadrature rules for approximation of real definite integrals in Adaptive environment , Proceedings of the International Multi Conference of Engineers and Computer Scientists,I,202-205,(2011).

Dash, R.B. and Das, D., Application of Mixed quadrature rules in the Adaptive Quadrature Routine, Gen. Math. Notes, Vol. 18(1), (2013), pp. 46-63.

Dash, R.B. and Das, D., On the use of Mixed quadrature in Adaptive quadrature Routines Global Journal of Mathematics and Mathematical Sciences, Research India Publications Vol-2 Number 1(2012), pp. 45-56.

Singh, B.P. and Dash, R.B., Application of Mixed quadrature rules using anti-Gaussian Quadrature rule in Adaptive Quadrature, Journal of the Orissa mathematical Society,33(2) ,61-70,(2014).

Singh, B.P. and Dash, R.B., Forming two Mixed Quadrature rules using anti-Gaussian Quadrature rule, International J. of Math. Sci. and Engg. Appls. (IJMESA),09( iv),27-38,(2015).

Clenshaw, C.W. and Curties , A.R., A method 700 numerical integration on an automatic computer, Numer. Math.,2,197-205,(1960) MR 22:8659.




DOI: http://dx.doi.org/10.6084/ijact.v5i6.581

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