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

Authors:
V. I. Tselyaev
Affiliations:
Nuclear Physics Department, V. A. Fock Institute of Physics, St. Petersburg State University, Petrodvorets 198504, St. Petersburg, Russia
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

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.