Implementation of Shishkin mesh in the modelling of spring-mass system

Abstract

In this article we will analyze the model of spring-mass system with very large damping or very small mass as well as its numerical solution. In the first part of the work we will derive the model with initial conditions and discuss the behavior of the exact solution. In the next part we will analyze the numerical solution using the finite difference method and in the last part of the work we will implement the Shishkin mesh in the numerical scheme and comment the error of approximation.