Adaptive quadrature for sharply spiked integrands

摘要

A new adaptive quadrature algorithm that places a greater emphasis on cost reduction while still maintaining an acceptable accuracy is demonstrated. The different needs of science and engineering applications are highlighted as the existing algorithms are shown to be inadequate. The performance of the new algorithm is compared with the well known adaptive Simpson, Gauss-Lobatto and Gauss-Kronrod methods. Finally, scenarios where the proposed algorithm outperforms the existing ones are discussed.