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Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations

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Abstract

Some embedded Runge-Kutta methods for the numerical solution of the eigenvalue Schrödinger equation are developed. More specifically, a new embedded modified Runge-Kutta 4(6) Fehlberg method with minimal phase-lag and a block embedded Runge-Kutta-Fenlberg method are developed. For the numerical solution of the eigenvalue Schrödinger equation we investigate two cases. (i) The specific case, in which the potential V x is an even function with respect to x. It is assumed, also, that the wavefunctions tend to zero for x → ± ∞. (ii) The general case for the well-known cases of the Morse potential and Woods-Saxon or Optical potential. Numerical and theoretical results show that the new approaches are more efficient compared with the well-known Runge-Kutta-Fehlberg 4(5) method.

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  1. Section of Mathematics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, GR-671 00, Xanthi, Greece E-mail:

    T.E. Simos

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Simos, T. Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations. Journal of Mathematical Chemistry 24, 23–37 (1998). https://doi.org/10.1023/A:1019102131621

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