In this paper, a numerical solution of one-dimensional time-dependent advection-diffusion equation with variable coefficients in semi-infinite domain is presented by using the differential quadrature method. Both the explicit and implicit approaches are provided. Totally, two solute dispersion problems are employed to simulate various conditions. The inhomogeneity of the domain is supplied by the spatially dependent flow. The problem domains are modeled with Chebyshev-Gauss-Lobatto grid points. In order to examine the accuracy and the efficiency of the suggested explicit and implicit approaches, analytical solutions, which are presented in the literature, are employed. In addition, the results of the above-mentioned method are compared with outcomes of the finite difference method. The results show that both of the explicit and implicit forms of the differential quadrature method are efficient, robust and reliable. But between these two forms, numerical predictions of implicit form are more accurate than explicit form. (C) 2016 Elsevier B.V. All rights reserved.