The object of this paper is to develop an accurate combined spectral collocation approach to numerically solve the generalized nonlinear Benjamin–Bona–Mahony–Burgers equation. The first stage is devoted to discretization in time, which is carried out with the aid of the well-known Taylor series expansions. Then the spectral collocation procedure based on the Boubaker polynomials is applied for the resulting discretized spatial operator in each time step. A detailed error analysis of the presented technique is carried out with regard to the space variable. The advantages of the hybrid technique are shown via performing several simulations through four test examples. Comparisons between our numerical results and the outcomes of some existing schemes indicate that the proposed technique is not only simple and easy-to-implement, but also sufficiently accurate using a moderate number of bases and a large time step
