Adaptive Quadrature

Abstract Adaptive quadrature is a powerful tool for numerical integration and involves a careful selection of the points where the integrand f ( x ) is evaluated such that the approximation to the definite integral is within some specified error tolerance. After motivating the need for adaptive quadrature by providing a brief overview of numerical quadrature, the basic principles of adaptive quadrature are introduced. The most well‐known adaptive quadrature method, adaptive Simpson rule, is presented with an accompanying example before concluding with a discussion and extension of the example to another widely used adaptive method, Gauss–Kronrod quadrature.