Modified Runge-Kutta Phase-fitted Methods

4 Modified Runge-Kutta Phase-fitted Methods. - Simos et al. have considered a modified four-stage exphcit Runge-Kutta method presented in Table 12. The parameters of the method are given by  

The free parameter gi is determined in order that the method has phase-lag of order infinity (see ref 6 for more details on phase-lag analysis of Runge-Kutta methods). 

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In [15], [26], [32], [59]-[60], [72] some modified Runge-Kutta or Runge-Kutta-Nystrom methods are constructed. The modification is based on exponential and trigonometric fitting or phase-fitting property. 

Table 12 The modified four-stage explicit phase-fitted Runge-Kutta method of Simos et al.

T. E. Simos and J. Vigo-Aguiar, A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrodinger equation. Journal of Mathematical Chemistry, 2001, 30(1), 121—131. 

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