A generalized Numerov method for linear second-order differential equations involving a first derivative term

The Numerov method for linear second-order differential equations is generalized to include equations containing a first derivative term. The method presented has the same degree of accuracy as the conventional Numerov method. The accuracy of the method is analysed in a limiting case and in the framework of the numerical experiment in comparison with the Runge–Kutta method and with another modifications of the Numerov method. A general scheme of the application to the numerical solution of the Hartree–Fock equations is considered.