Termination Criterion and error analysis of a mixed rule using an anti-Lobatto rule in whole interval and adaptive algorithm

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-48 Number-2
Year of Publication : 2017
Authors : Bibhu Prasad Singh, Dr. Rajani Ballav Dash
  10.14445/22315373/IJMTT-V48P512

MLA

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). V48(2):98-107 August 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
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.

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Keywords
Anti-Lobatto rule, Lobatto rule, Fejer’s rule , mixed rule , adaptive algorithm,error analysis, termination criterion.