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Construction of Trigonometrically and Exponentially Fitted Runge–Kutta–Nyström Methods for the Numerical Solution of the Schrödinger Equation and Related Problems – a Method of 8th Algebraic Order |
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| Authors: | Z. Kalogiratou T.E. Simos |
| Affiliation: | (1) Department of International Trade, Technological Educational Institute of Western Macedonia at Kastoria, P.O. Box 30, GR-521 00 Kastoria, Greece;(2) Section of Mathematics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece |
| Abstract: | General conditions are presented for an m-stage Runge–Kutta–Nyström fitting to exponential and trigonometric functions. As an example an 8th order Runge–Kutta–Nyström method is constructed. Numerical results on the numerical solution of the Schrödinger equation and related problems indicate that the new method is more accurate than the classical one (we call classical Runge–Kutta–Nyström method the corresponding method with constant coefficients). |
| Keywords: | trigonometrically-fitted exponentially-fitted Runge– Kutta– Nyströ m Schrö dinger equation scattering problems resonance problem periodic solutions oscillating solutions |
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