# New multiple stages multistep method with best possible phase properties for second order initial/boundary value problems

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## Abstract

A new multiple stages multistep method with best possible phase and stability properties is recommended, for the first time in the literature. A detailed theoretical and numerical analysis is also developed. The capacity of the new algorithm is tested by applying it on the solution of the solution of the Schrödinger equation.

## Keywords

Schrödinger equation Multistep methods Multistage methods Interval of periodicity Phase-lag Phase-fitted Derivatives of the phase-lag## Mathematics Subject Classification

65L05## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## Supplementary material

10910_2018_986_MOESM1_ESM.pdf (189 kb)

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