High Order Phase Fitted Multistep Integrators for the Schrödinger Equation with Improved Frequency Tolerance
This work provides an incremental improvement in numerical integration methods for quantum mechanical simulations, specifically for the Schrödinger equation.
The authors developed a new family of 14-step linear multistep methods for the Schrödinger equation that improve frequency tolerance by flattening the phase lag function near the fitted frequency, with efficiency demonstrated through error analysis and numerical tests.
In this work we introduce a new family of 14-steps linear multistep methods for the integration of the Schrödinger equation. The new methods are phase fitted but they are designed in order to improve the frequency tolerance. This is achieved by eliminating the first derivatives of the phase lag function at the fitted frequency forcing the phase lag function to be '\textit{flat}' enough in the neighbor of the fitted frequency. The efficiency of the new family of methods is proved via error analysis and numerical applications.