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

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

2008-11-15

arxiv.org/abs/0811.2476v1

Mathematics

Numerical Analysis

36 pages, 6 figures

Scientific paper

In this work we introduce a new family of twelve-step linear multistep methods for the integration of the Schr\"odinger 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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