High Order Phase Fitted Multistep Integrators for the Schr\"odinger Equation with Improved Frequency Tolerance

TL;DR

This paper introduces a new family of high-order multistep integrators for the Schrödinger equation that are phase fitted with enhanced frequency tolerance, improving accuracy near the fitted frequency.

Contribution

A novel 14-step linear multistep method with improved frequency tolerance by eliminating derivatives of the phase lag function, enhancing stability and accuracy.

Findings

Methods demonstrate high accuracy in numerical tests

Enhanced frequency tolerance compared to previous methods

Error analysis confirms theoretical improvements

Abstract

In this work we introduce a new family of 14-steps linear multistep methods for the integration of the Schr\"odinger 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.