Application of Mixed Quadrature Rules 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 have been used for fixing termination criterion in adaptive quadrature routines. Three mixed quadrature rules are constructed for this purpose. The first is the convex combination of Lobatto 4-point rule and the Clenshaw-Curtis 5-point rule, the second is the linear combination of the first mixed quadrature rule and the Lobatto 5-point rule and the third is the linear combination of the second mixed quadrature rule and the Kronrod extension of Lobatto 4-point rule. Adaptive quadrature routines being recursive by nature, a termination criterion is formed taking into account the three 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.