A refined machinery to calculate large moments from coupled systems of linear differential equations

TL;DR

This paper introduces refined techniques for the large moment method, enabling the calculation of many moments from coupled linear differential systems while minimizing the need for initial values, thus improving efficiency.

Contribution

The paper presents improved versions of the large moment method that significantly reduce the number of initial values required for computations.

Findings

Refined algorithms decrease initial value requirements

Enhanced method increases computational efficiency

Applicable to physical systems modeled by differential equations

Abstract

The large moment method can be used to compute a large number of moments of physical quantities that are described by coupled systems of linear differential equations. Besides these systems the algorithm requires a certain number of initial values as input, that are often hard to derive in a preprocessing step.Thus a major challenge is to keep the number of initial values as small as possible. We present the basic ideas of the underlying large moment method and present refined versions that reduce significantly the number of required initial values.