An adaptive Simpson quadrature algorithm for learning purposes

Abstract

A student is taught the advantages of adaptive quadrature over traditional numerical integration, but in practice, he cannot verify these for himself because of the complexity involved in programming such algorithms. In an attempt to overcome some of the programming difficulties, various books, see [1, 2], compromise by recommending a restricted number of nested subintervals. However, while such a compromise alleviates the storage problem, it may, in the case of ‘badly‐behaved’ integrands, prove to be too restrictive and thus destroy the concept of adaptive quadrature. This paper introduces an adaptive quadrature algorithm that demands neither storing strategies, nor a preset limit on the number of subdivisions. The algorithm is simple enough to be manipulated by undergraduates. A FORTRAN listing of the algorithm is included in this paper.