具有改进相位滞后特性的高阶多步法用于薛定谔方程积分
High Order Multistep Methods with Improved Phase-Lag Characteristics for the Integration of the Schrödinger Equation
AI总结：
本文提出一种通过消除相位滞后函数及其一阶导数在特定频率处的值来改进相位滞后特性的十二步线性多步法，用于薛定谔方程积分，并通过误差分析和数值应用证明了其有效性。
摘要：
本文提出了一族新的十二步线性多步法，用于薛定谔方程的积分。新方法采用一种新的方法论构建，通过消除相位滞后函数及其一阶导数在特定频率处的值来改进相位滞后特性。这降低了积分方法对问题估计频率的敏感性。通过误差分析和数值应用证明了新方法族的高效性。
英文摘要：
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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