Wave propagation is considered on surface fluid flowing in an inclined channel. The model is shallow water equations extended by involving the bed inclination and bottom friction. The model is solved numerically by predictor-corrector third-order Adam-Bashforth-Moulton (ABM) method to observe the wave deformation. Before applying the method, numerical stability of this scheme is studied so that we obtain a stable scheme. As a result, we found that the  initial wave deforms by increasing the amplitude until a certain value forming the type of roll wave. The computed roll waves show satisfactory agreement with the analytical solution of roll waves.

shallow water equations, roll waves, Adam-Bashforth-Moulton method.