Thread: predictor-corrector scheme

Hi!
I'm asking for help to understand the realization of the iterative predictor-corrector scheme (I'm not a specialist in this field) for PDE system . The description of a method attached in article.
The question concerns algorithm realization under the formula (A5), resulted in article
(A5)
where - function in the right part of the equations, and - variables.
, as I have understood, these are predicted value of all variables from, for example, Euler's method. Then it is necessary to calculate variables and to compare them with predicted, repeating algorithm before achievement of necessary accuracy. But how to calculate if in the right part there are the same , for me not clearly? In any way I don't understand the dependence of two variables means? How to use this formula in calculations? I will be glad to any concrete algorithms or the references to it.
Wait for your suggestions.