The effect of finite difference approximations in solving Dirichlet boundary value problem

摘要

Finite difference approximations are used to approximate derivatives of functions numerically when the functional values are known. These approximations are used to solve differential equations with certain order of accuracy. The level of accuracy is subject to fail for the higher order. Hence it is necessary to analyse the limit of the order of accuracy. In this work, the effect of higher order finite difference approximations are analysed to solve second order linear ordinary differential equations with Dirichlet's boundary conditions. The limitations of solving a Dirichlet boundary value problem using finite difference approximation are also discussed.