High Order Multistep Methods with Improved Phase-Lag Characteristics for the Integration of the Schrödinger Equation

2008/11/15 by D. S. Vlachos, Vlachos, D. S., Zacharias Anastassi +3
Engineering · Mathematics · #65L05 #65L06 #81Q05 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.0811.2476

openalex publication_date 2008/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we introduce a new family of twelve-step linear multistep methods for the integration of the Schrödinger 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.

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