Applied Mathematics & Information Sciences

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The purpose of this paper is the development of an explicit linear sixth algebraic order six-step methods with vanished phaselag and its first and second derivatives. The development of the new method is based on a theoretical and computational investigation. The theoretical investigation consists : –The construction of the method –The determination of the local truncation error –The comparative local truncation error analysis –The stability analysis We note here that the stability analysis is is based on a scalar test equation with different frequency than the frequency of the scalar test equation used for the phase-lag analysis. The computational investigation of the new proposed method consists the application of the new obtained method to the resonance problem of the radial time independent Schr¨odinger equation. Based on the above mentioned studies we conclude that the new developed linear six-step method is more efficient (computationally and theoretically) than other well known methods for the approximate integration of the Schr¨odinger equation and related periodical/oscillatory initial or boundary value problems.