A numerical scheme for diffusion-convection equation with piecewise constant arguments

This article is concerned with using a finite difference method, namely the θ-methods, to solve the diffusion-convection equation with piecewise constant arguments.The stability of this scheme is also obtained. Since there are not many published results on the numerical solution of this sort of differential equation and because of the importance of the above equation in the physics and engineering sciences, we have decided to study and present a stable numerical solution for the above mentioned problem. At the end of article some experiments are done to demonstrate the stability of the scheme. We also draw the figures for the numerical and analytical solutions which confirm our results.The numerical solutions have also been compared with analytical solutions.