Termination criterion and error analysis of a mixed rule using an anti-gaussian rule in whole interval and adaptive algorithm Singh Bibhu Prasad1, Dr. Dash Rajani Ballav2 1Institute of Mathematics and Application, Andharua, Bhubaneswar, Odisha, India, E-mail: bpsmath78@gmail.com 2Ex Reader in Mathematics, Ravenshaw University, Cuttack, Odisha, India. E-mail: rajani_bdash@rediffmail.com *Corresponding Author: Bibhu Prasad Singh, Institute of Mathematics and Application, Andharua, Bhubaneswar, Odisha, 751003, India. E-mail: bpsmath78@gmail.com
2000 Mathematics Subject Classification: 65D30, 65D32 Online published on 16 January, 2018. Abstract A mixed quadrature rule of higher precision for approximate evaluation of real definite integrals has 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. Top Keywords Anti-Gaussian rule, Gaussian rule, Boole's rule, mixed rule, adaptive algorithm, error analysis, termination criterion. Top |