Coupled Parabolic PDE Example

To further demonstrate the simplicity and the straightforward nature of the orthogonal collocation method, we consider the adsorption problem dealt with in Section 12.2 where the singular perturbation approach was used. The nondimensional mass balance equations are 

we note the symmetry eondition at jc = 0 and make the symmetry transformation u = x. in terms of this new variable, the mass balance equations are 

Our objective here is to obtain the mean adsorbed concentration versus time. In nondimensional form, this mean concentration is given by 

Written in terms of the u variable, the above equation becomes 

The mass balance equation (Eqs. 12.215a) is valid in the interior of the domain thus, we evaluate it at the ith interior collocation point (i = 1,2,3. A) and obtain 

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