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Termination Criterion and Error Analysis of a Mixed Rule Using an Anti-Gaussian Rule in Whole Interval and Adaptive Algorithm

Journal: International Journal of Scientific Engineering and Research (IJSER) (Vol.5, No. 8)

Publication Date:

Authors : ; ;

Page : 37-45

Keywords : Anti-Gaussian rule; Gaussian rule; Fejer?s rule; mixed rule; adaptive algorithm; error analysis; termination criterion;

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Mixed quadrature rules of higher precision for approximate evaluation of real definite integrals have been constructed using an anti-Gaussian 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-Gaussian 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.

Last modified: 2021-07-08 16:11:07