An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes

Abstract An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162–170, 1980) of adaptive type based on the Newton–Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991; ACM Trans. Math. Softw. 17:218–232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229–259. Academic, Orlando, FL, 1971).Keywords Automatic quadrature · Adaptive algorithm · Numerical comparison