Convergence Rates of Finite Difference Schemes for the Diffusion Equation with Neumann Boundary Conditions

Abstract

In this paper, we consider the convergence rates of the Forward Time, Centered Space (FTCS) and Backward Time, Centered Space (BTCS) schemes for solving one-dimensional, time-dependent diffusion equation with Neumann boundary condition. We present the derivation of the schemes and develop a computer program to implement it. The consistency and the stability of the schemes are described. By the support of the numerical problems convergence rates of the schemes have been determined. It is found that both methods are first order accurate in the spatial dimension in 𝐿𝐿∞ - norm