On simulations of the classical harmonic oscillator equation by difference equations

Jan L. Cieśliński, Bogusław Ratkiewicz
2006 Advances in Difference Equations  
We discuss the discretizations of the second-order linear ordinary diffrential equations with constant coefficients. Special attention is given to the exact discretization because there exists a difference equation whose solutions exactly coincide with solutions of the corresponding differential equation evaluated at a discrete sequence of points. Such exact discretization can be found for an arbitrary lattice spacing.
doi:10.1155/ade/2006/40171 fatcat:tiwbij6u3fbxjo2nr7qltj6bvq