In this paper, we studied the horizontal imbibition phenomenon. We looked at a numerical method for solving a nonlinear partial differential equation that was caused by the imbibition phenomenon. With the aid of appropriate beginning and boundary conditions, we were able to approximate the solution of the governing equation using the variable separable approach, the homotopy perturbation method, and the polynomial-based differential quadrature method. We came to the conclusion that, when compared to some traditional approaches, such as the Homotopy perturbation method and the variable separable method with a smaller number of grid points, the polynomial-based differential quadrature method provides a better approximation solution.