High order multistep methods with improved phase-lag characteristics for the integration of the Schr?dinger equation

In this work we introduce a new family of 12-step linear multistep methods for the integration of the Schr?dinger equation. The new methods are constructed by adopting a new methodology which improves the phase lag characteristics by vanishing both the phase lag function and its first derivatives at a specific frequency. This results in decreasing the sensitivity of the integration method on the estimated frequency of the problem. The efficiency of the new family of methods is proved via error analysis and numerical applications. T. E. Simos is a highly cited researcher, active member of the European Academy of Sciences and Arts. Corresponding member of the European Academy of Sciences, corresponding member of European Academy of Arts, Sciences and Humanities.