Application of the generalized finite difference method to solve the advection–diffusion equation

The study of the advection–diffusion equation continues to be an active field of research. The subject has important applications to fluid dynamics as well as many other branches of science and engineering.This paper shows the application of the generalized finite difference method to solve the advection–diffusion equation by the explicit method. The convergence of the method has been studied and the truncation error over irregular grids is given. An example has been solved using the explicit finite difference formulae and the criterion of stability.