An explicit linear six-step method with vanished phase-lag and its first derivative

An explicit linear sixth algebraic order six-step method with vanished phase-lag and its first derivative is constructed in this paper. We will study the method theoretically and computationally. Theoretical investigation contains the building of the method, the calculation of the local truncation error, the comparative error analysis of the new method with the method with constant coefficients and the stability analysis of the new method using scalar test equation with different frequency than the frequency of the scalar test equation used for the development of the method. Computational investigation contains the application of the new obtained linear six-step method to the resonance problem of the radial time independent Schrödinger equation. The theoretical and computational study lead us to the summary that the new proposed linear scheme is computationally and theoretically more efficient than other well known methods for the numerical solution of the Schrödinger equation and related periodic initial or boundary value problems.