A family of explicit linear six-step methods with vanished phase-lag and its first derivative

A family of explicit linear sixth algebraic order six-step methods with vanished phase-lag and its first derivative is obtained in this paper. The investigation of the above family of methods contains:

theoretical study of the new family of methods and

computational study of the new family of methods.

The theoretical study of the above mentioned family of methods contains:

1. the development of the method,
2. the computation of the local truncation error,
3. the comparative local truncation error analysis. The comparison is taken place between the new family of methods with the corresponding method with constant coefficients and
4. the stability analysis of the new family of methods. The stability analysis is taken place using test equation with different frequency than the frequency of the test equation used for the phase-lag analysis of the methods.

The application of the new family of linear six-step sixth algebraic order methods to the resonance problem of the one-dimensional time independent Schrödinger equation is used for the computational study of the new family of methods. The result of the above mentioned theoretical and computational investigation is that the new proposed family of linear explicit schemes are computationally and theoretically more effective than other well known methods for the approximate solution of the radial Schrödinger equation and related initial or boundary value problems with periodic and/or oscillating solutions.