The recursive adaptive quadrature in MS Fortran-77

Abstract

It is shown that MS Fortran-77 compilers allow to construct recursive subroutines. The recursive one-dimensional adaptive quadrature subroutine is considered in particular. Despite its extremely short body (only eleven executable statements) the subroutine proved to be very effective and competitive. It was tested on various rather complex integrands. The possibility of function calls number minimization by choosing the optimal number of Gaussian abscissas is considered. The proposed recursive procedure can be effectively applied for creating more sophisticated quadrature codes (one- or multi-dimensional) and easily incorporated into existing programs.