An efficient wavelet based approximation method to water quality assessment model in a uniform channel

In this paper, we have developed an efficient shifted second kind Chebyshev wavelets based approximation method to water quality assessment model problem. The governing equation of the uniform flow model is one-dimensional convection diffusion equation (CDE) with variable coefficients. This water quality model requires the calculation of the substance dispersion given the water velocity in the channel. To the best of our knowledge, until now there is no rigorous wavelet solution has been reported for the water quality model problem. The shifted second kind Chebyshev wavelet method (CWM) for assessment of the chemical oxygen demand (COD) in a river is considered. Some numerical examples are presented to demonstrate the validity and applicability of the method.