A New Phase Fitted Method

1 A New Phase Fitted Method. - Consider the one free parameter symmetric three-step hybrid predictor-corrector explicit method  

Applying the above method to the scalar test equation 

In Table 4 we present the properties of the phase fitted methods. 

4 Numerical Illustrations for Exponentially-Fitted Methods and Phase Fitted Methods. - In this section we test several finite difference methods with coefficients dependent on the frequency of the problem to the numerical solution of resonance and eigenvalue problems of the Schrodinger equations in order to examine their efficiency. First, we examine the accuracy of exponentially-fitted methods, phase fitted methods and Bessel and Neumann fitted methods. We note here that Bessel and Neumann fitted methods will also be examined as a part of the variable-step procedure. We also note that Bessel and Neumann fitted methods have a large penalty in a constant step procedure (it is known that the coefficients of the Bessel and Neumann fitted methods are position dependent, i.e. they are required to be recalculated at every step). 

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