Volterra method for the radial Schrödinger equation

摘要

A new Volterra type integral equation method for the numerical solution of the radial Schrödinger equation is investigated. The method, carried out in configuration space, is based on the conversion of differential equations into a system of Volterra type integral equations together with the application of a spectral type Clenshaw–Curtis quadrature. Through numerical examples, the Volterra type integral equation method is shown to be more efficient and more accurate than the integral equation method based on the Fredholm formulation (J. Comput. Phys. 134 (1997) 134) and better than finite difference methods. Accompanying C++ code for the Volterra type method is available upon request.