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A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation. (English) Zbl 1003.65082
Summary: A modified phase-fitted Runge-Kutta method (i.e., a method with phase-lag of order infinity) for the numerical solution of periodic initial-value problems is constructed. This new modified method is based on the Runge-Kutta fifth algebraic order method of {\it J. R. Dormand} and {\it P. J. Prince} [J. Comput. Appl. Math. 6, 19--26 (1980; Zbl 0448.65045)]. The numerical results indicate that this new method is more efficient for the numerical solution of periodic initial-value problems than the well known Runge-Kutta method of Dormand and Prince [loc. cit.] with algebraic order five.

65L06Multistep, Runge-Kutta, and extrapolation methods
34L40Particular ordinary differential operators
65L05Initial value problems for ODE (numerical methods)
34C25Periodic solutions of ODE
34A34Nonlinear ODE and systems, general
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