Stability and Consistency Analysis for Central Difference Scheme for Advection Diffusion Partial Differential Equation

Abel Kurura Tinega, Charles Otieno Ndede

Abstract: The paper studies stability and consistency analysis for one-dimensional advection diffusion equation using the Central Difference Scheme (CDS). Taylor's series expansion is used to expand the finite difference approximations in the CDS scheme and it is found out that the scheme is consistent with the model equation. Von-Neumann Method is used to analyze the stability of the CDS scheme developed and the scheme is found to be conditionally stable.

Keywords: Advection diffusion equation ADE, Partial Differential Equations PDEs, Central difference scheme CDS, Forward time backward space and centered space FTBSCS and forward time and centered Space FTCS and Stability condition