Construction of new Non-standard Finite Difference Schemes for the Solution of a free un-damped Harmonic Oscillator Equation

Abstract

In this paper we discussed the numerical solution to the model of a freely suspended spring with a mass attached. Suitable nonstandard finite difference schemes were developed  for the solution of the resulting dynamical system which follows a free un-damped harmonic oscillator. The result of the numerical experiment  on the schemes are illustrated  with 3D graphs .

Keywords: Numerical methods , Non-Local Approximations,  Non-standard finite difference schemes, Qualitative properties, Free un-damped Harmonic Oscillator,  Monotonicity of solution.