Solution of convection-diffusion model in groundwater pollution

This research involves the development of the spectral collocation method based on orthogonalized Bernoulli polynomials to the solution of time-fractional convection-diffusion problems arising from groundwater pollution. The main aim is to develop the operational matrices for the fractional derivative and classical derivatives. The advantage of our approach is to orthogonalize the Bernoulli polynomials for the sake of creating sparse operational matrices in such a way that classical derivatives have one sub-diagonal non-zero entries only, and also creating an operational matrix for fractional derivative have diagonal matrix only. Due to these properties, the cost of computational our approach is very low and the convergence is fast. A discussion on the error analysis for the presented approach is given. Two test problems are considered to illustrate the effectiveness and applicability of our method. The absolute error in the computed solution compares with the existing method in the literature. The comparison shows that our method is more accurate and easily implemented.