Numerical Simulation of the Harmonic Oscillator Differential Equation Using Finite Difference Schemes

Abstract

In this study, we have developed a new type of finite difference scheme using dynamically renormalized denominator functions and trigonometric and exponential interpolating functions. These schemes show local stability, convergence, and consistency. The model provides an improved numerical scheme for the Harmonic Oscillator Differential Equation. Additionally, we compared the new model with a previous discrete model for the Harmonic equation and also confirmed the suitability of the new schemes for the numerical simulation of the tested problems.