In this project, the derivation of the Forward Time, Centered Space (FTCS) is also called the explicit scheme and Backward Time, Centered Space (BTCS) is also called the implicit scheme for solving one-dimensional, time-dependent diffusion equation with Neumann boundary conditions are presented. The consistency, stability and convergence of these schemes are also analyzed and thus the schemes are convergent. By taking the numerical examples convergence rates of the schemes are determined using the maximum norm ( ). To implement the schemes for the numerical examples practically, a computer program (Matlab) is used. It is found that both the Explicit and implicit schemes are first – order accurate in the spatial dimension regardless of the actual order of the diffusion equation by the effect of the Neumann boundary conditions.