A New Family of Multistep Methods with Improved Phase Lag Characteristics for the Integration of Orbital Problems

TL;DR

This paper introduces a new family of ten-step linear multistep methods designed to improve phase lag characteristics for orbital problem integration, enhancing accuracy through a novel methodology.

Contribution

The paper presents a novel methodology for constructing multistep methods that optimize phase lag properties by vanishing the phase lag function and its derivatives at a specific frequency.

Findings

Enhanced phase lag performance demonstrated

Error analysis confirms improved accuracy

Numerical applications validate the methods' efficiency

Abstract

In this work we introduce a new family of ten-step linear multistep methods for the integration of orbital problems. 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. The efficiency of the new family of methods is proved via error analysis and numerical applications.