Quadrature rules for approximating semi-integrals and semiderivatives

摘要

Quadrature methods are developed for the numerical approximation of half-order integrals and derivatives. The Riemann- Liouville definition of a semi-integral is the starting point for the analysis. Numerical integration methods based on classical quadrature theory and piecewise cubic Hermite interpolation are explored. Numerical examples and a FORTRAN subroutine are provided to illustrate the theory.