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

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 Vx 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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