Document Type : Research Paper
Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Faculty of Mathematical Sciences, Department of Applied Mathematics and Computer Science, University of Guilan, Rasht, Iran.
This article is concerned with using a ﬁnite difference method, namely the theta-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 ou results.The numerical solutions have also been compared with analytical solutions.