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India | Mathematics | Volume 5 Issue 8, August 2017 | Pages: 37 - 45
Termination Criterion and Error Analysis of a Mixed Rule Using an Anti-Gaussian Rule in Whole Interval and Adaptive Algorithm
Abstract: 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.
Keywords: Anti-Gaussian rule, Gaussian rule, Fejer?s rule, mixed rule, adaptive algorithm, error analysis, termination criterion
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