Application of two mixed Quadrature rules using an anti-Gaussian Quadrature rule in the Adaptive quadrature routine

A model is set up which embodies the basic features of Adaptive quadrature routines involving mixed rules. Not before mixed quadrature rules basing on anti-Gaussian quadrature rule have been used for fixing termination criterionin Adaptive quadrature routines. Two mixed quadrature rules of higher precision for approximate evaluation of real definite integrals have been constructed using an anti-Gaussian rule for this purpose. The first is linear combination of anti-Gaussian three point rule and Fejers three point first rule, the second is the linear combination of anti-Gaussian three point rule and Fejers three point second rule.The analytical convergence of the rules have been studied. The error bounds have been determined asymptotically. Adaptive quadrature routines being recursive by nature, a termination criterion is formed taking in to account two mixed quadrature rules. The algorithm presented in this paper has been “C” programmed and successfully tested on different integrals. The efficiency of the process is reflected in the table at the end.