International Journal of Mathematics Trends and Technology
Volume 48 | Number 2 | Year 2017 | Article Id. IJMTT-V48P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V48P512
A mixed quadrature rule of higher precision for approximate evaluation of real definite integrals have been constructed using an anti-Lobatto rule. The analytical convergence of the rule has been studied. The error bounds have been determined asymptotically. In adaptive quadrature routines not before mixed quadrature rules basing on anti-Lobatto quadrature rule have been used for fixing termination criterion .Adaptive quadrature routines being recursive by nature ,a termination criterion is formed taking in to account a mixed quadrature rule. The algorithm presented in this paper and successfully tested on different integrals by C program. The relative efficiency of the mixed quadrature rule is reflected in the table at the end .
[1] Dirk P. Laurie, Anti-Gaussian quadrature formulas, mathematics of computation,65(1996)pp. 739-749.
[2] Dirk P. Laurie, Computation of Gauss-type quadrature formulas, Journal of Computational and Applied mathematics of computation,127(2001)pp. 201-217.
[3] Dirk P. Laurie, Stopping functionals for Gaussian quadrature formulas, Journal of Computational and Applied mathematics ,127(2001)pp. 153-171.
[4] Dirk P. Laurie, Sharper error estimates in adaptive quadrature, BIT,(1983)CMP,23:258-261,MR84e:65027.
[5] Dirk P. Laurie, Practical error estimation in numerical integration, Journal of Computational and Applied mathematics ,(1985)CMP,17:14,12 and 13:258-261.
[6] J. Berntsen, Practical error estimation in adaptive multidimensional quadrature routines, Journal of Computational and Applied mathematics,25(1989),327-340,North-Holland.
[7] J. Berntsen, T.O. Espelid and T.Sorevik.,On the subdivision strategy in adaptive quadrature algorithms, Journal of Computational and Applied mathematics ,35(1991),119-132.
[8] S. Conte. and C.D. Boor., Elementary numerical analysis , Mc-Graw Hill, (1980).
[9] C.W.Clenshaw and A.R.Curties, A method 700 numerical integration on an automatic computer,Numer.Math,2 ,(1960),MR22:8659,197-205.
[10] F. Lether ., On Birkhoff-Young quadrature of analytic function, J. Comp. Applied Math.2, 2(1976) , pp.81-84 .
[11] Atkinson Kendall E.,An introduction to numerical analysis , 2nd edition ,John Wiley and Sons,Inc, (1989).
[12] A.C.Genz and A.A.Malik(*).,Remark on algorithm 006: An adaptive algorithm numerical integration over an N-dimensional rectangular region, Journal of Computational and Applied mathematics , (1980),volume 6,No 4.
[13] P.V. Dooren and L.de. Ridder.,An adaptive algorithm numerical integration over an n-dimensional cube, Journal of Computational and Applied mathematics , (1976),volume 2,No 3.
[14] B.P. Acharya and R.N. Das., Compound Birkhoff –Young rule for numerical integration of analytic functions.Int.J.math.Educ.Sci.Technol 14(1983),pp.91-101.
[15] R.N. Das and G. Pradhan ., A mixed quadrature rule for approximate value of real definite Integrals, Int. J. Edu. Sci. Technol, 27 (1996), pp. 279 - 283.
[16] R.N. Das and G. Pradhan .,A mixed quadrature Rule for Numerical integration of analytic functions, Bull. Cal. Math. Soc., 89(1997) ,pp.37 - 42.
[17] A. Begumisa and I. Robinson., Suboptional Kronrod extension formulas for Numerical quadrature , math, MR92a(1991),pp.808-818.
[18] Walter. Gautschi., Gauss-Kronrod quadrature –a survey, In G.V. Milovanovic. Editor, Numerical Methods and Approximation Theory III, University of Nis (1988) . MR89k:41035,pp.39-66.
Bibhu Prasad Singh, Dr. Rajani Ballav Dash, "Termination Criterion and error analysis of a mixed rule using an anti-Lobatto rule in whole interval and adaptive algorithm," International Journal of Mathematics Trends and Technology (IJMTT), vol. 48, no. 2, pp. 98-107, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V48P512
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