In the most general case, suppose we have a set of N nonlinear equations

(21–1)

where is a vector of unknowns. When tearing is applied to Equation 21–1 it is rewritten as:

(21–2)

where

(21–3)

The problem (Equation 21–2 ) is solved using an inner-outer iteration where in each outer iteration is solved for alone and for each inner iteration, is solved for Y alone with held fixed at value from the previous solution of .

It is important that the choice of , and is done using knowledge of the underlying mathematical model so that the tears make engineering sense. Otherwise the inner-outer solution to Equation 21–2 may not converge or give a solution that is not a solution of Equation 21–1 .