A principal possibility for computer investigation of evolution of dynamical systems with independent on time accuracy

TL;DR

This paper introduces a novel method using Laplace transforms and computer algebra to analyze the evolution of perturbed Hamiltonian systems with accuracy that does not degrade over time.

Contribution

It presents a new approach for studying dynamical systems that maintains consistent accuracy throughout the evolution, unlike traditional methods.

Findings

Method enables time-independent accuracy in evolution analysis.

Uses Laplace transform and computer algebra for analytical solutions.

Applicable to perturbed Hamiltonian systems in astrophysics.

Abstract

Extensive N-body simulations are among the key means for the study of numerous astrophysical and cosmological phenomena, so various schemes are developed for possibly higher accuracy computations. We demonstrate the principal possibility for revealing the evolution of a perturbed Hamiltonian system with an accuracy independent on time. The method is based on the Laplace transform and the derivation and analytical solution of an evolution equation in the phase space for the resolvent and using computer algebra.