On the exact discretization of the classical harmonic oscillator equation

TL;DR

This paper explores the precise numerical discretization of the classical harmonic oscillator equation, including inhomogeneous and multidimensional cases, emphasizing energy conservation and providing potential numerical applications.

Contribution

It introduces exact discretization methods for the harmonic oscillator, extending to complex cases and highlighting energy preservation, with practical numerical application suggestions.

Findings

Exact discretization formulas for harmonic oscillators.

Extension to inhomogeneous and multidimensional cases.

Potential for improved numerical simulations.

Abstract

We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. We present and suggest some numerical applications.