An Alternative Strategy for Cautions Adaptive Quadrature

An algorithm for adaptive quadrature is presented which attemptsto ensure that the quadrature used is valid for the behaviourof the integrand. This is achieved by using another algorithmto examine the finite differences of the integrand. The orderof the quadrature and the interval subdivision strategy usedform an integral part of this algorithm. The resulting adaptivequadrature algorithm is very reliable while its efficiency appearsto be of the order of other adaptive quadrature algorithms inthe literature.