New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation

Authors:
Z. Kalogiratou;Th. Monovasilis;T. E. Simos
Affiliations:
Department of Informatics and Computer Technology, Technological Educational Institute of Western Macedonia at Kastoria, P.O. Box 30, GR-521 00, Kastoria, Greece;Department of International Trade, Technological Educational Institute of Western Macedonia at Kastoria, P.O. Box 30, GR-521 00, Kastoria, Greece;College of Sciences, King Saud University, Department of Mathematics, P.O. Box 2455, Riyadh 11451, Saudi Arabia and Laboratory of Computational Sciences, Department of Computer Science and Technol ...
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 2
Cited 2

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Exponentially fitted explicit Runge-Kutta-Nyström methods

Journal of Computational and Applied Mathematics

A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation

Computers & Mathematics with Applications
Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations

Journal of Computational Physics

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Abstract

In this work we construct new Runge-Kutta-Nystrom methods especially designed to integrate exactly the test equation y^''=-w^2y. We modify two existing methods: the Runge-Kutta-Nystrom methods of fifth and sixth order. We apply the new methods to the computation of the eigenvalues of the Schrodinger equation with different potentials such as the harmonic oscillator, the doubly anharmonic oscillator and the exponential potential.