(National University of Lesotho, 2024-07-23) Kotoane, Bokang
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.