Error analysis for finite difference schemes

Abstract

Numerical methods are widely used in modern computations to approximate solutions to dif- ferential equations. There are many types of numerical methods that can be considered, but in this project, finite difference methods are considered. The underlying concept required for development of numerical schemes is taken into consideration. Numerical schemes are devel- oped and error analysis is always carried out for each scheme and solutions are developed using those schemes. in finding numerical solutions θ = 0, θ = 1, and θ = 1 2 are considered and they represent different schemes. It is found that the Crank-Nicholson scheme is the best performing finite difference scheme.