New threestages symmetric sixstep finite difference method with vanished phaselag and its derivatives up to sixth derivative for second order initial and/or boundary value problems with periodical and/or oscillating solutions
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Abstract
 1.
is a symmetric hybrid (multistages) sixstep method,
 2.
is of threestages,
 3.
is of twelfth algebraic order,
 4.
has vanished the phaselag and
 5.
has vanished the derivatives of the phaselag up to order six.

the construction of the new sixstep pair,

the presentation of the computed local truncation error of the new sixstep pair,
 the comparative error analysis of the new sixstep pair with other sixstep pairs of the same family which are:

the classical sixstep pair of the family (i.e. the sixstep pair with constant coefficients),

the recently proposed sixstep pair of the same family with vanished phaselag and its first derivative,

the recently proposed sixstep pair of the same family with vanished phaselag and its first and second derivatives,

the recently proposed sixstep pair of the same family with vanished phaselag and its first, second and third derivatives,

the recently proposed sixstep pair of the same family with vanished phaselag and its first, second, third and fourth derivatives and finally,

the recently proposed sixstep pair of the same family with vanished phaselag and its first, second, third, fourth and fifth derivatives


the stability and the interval of periodicity analysis for the new obtained sixstep pair and finally

the investigation of the accuracy and computational efficiency of the new developed sixstep pair for the solution of the Schrödinger equation.
Keywords
Schrödinger equation Multistep methods Multistage methods Interval of periodicity Phaselag Phasefitted Derivatives of the phaselagNotes
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
Supplementary material
References
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