Numerical computation of integrals with singularity in the adaptive integration scheme involving a mixed quadrature rule

A model is set up which embodies the basic features of adaptive quadrature routines involving a mixed rule. A mixed quadrature rule of precision five by blending Steffensen 4-point rule and Gauss-Legendre 2-point rule is constructed. Adaptive quadrature routines being recursive by nature, the termination criterion is given taking into account the Steffensen 4-point rule and the mixed rule. The algorithm presented in this paper is ‘C’ programmed and the inferences are illustrated by appropriate numerical examples.