Numerical Iterative Methods of Solution

Numerical Iterative Methods of Solution. There are a number of numerical methods that fall into this category but few have been applied to the solution of equation (16). The fact that no prior form of /(y) need be chosen is a distinct advantage. 

The regularization method described above may be applied in an iterative manner using the trial function approach described by Twomey. Instead of minimizing the curvature, the solution may be found by minimizing the sum of 

An approach that has met with success is the Adamson and Ling iterative method. This method converges to an acceptable solution much faster than any other iterative method although it is not a general iterative solution of the Fredholm equation since the initial approximation to /(y) is obtained by using the condensation approximation. Thus the method utilizes information concerning the physical form of the local isotherm functions (see Section 4 for details and applications). 

Another procedure that has been successful is that described by Ross and Morrison in which the adsorption isotherm on a patchwise heterogeneous 

In this application equation (42) is ill-conditioned and cannot be solved directly. However one can strive for as close agreement as possible between both sides of the equality. One way to do this is to minimize the sum of the squared relative deviation, Do (or r.m.s. deviation)  

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