And here we have the initial conditions.
In the above system of equations there are nine variables, namely u, w, p_w, s, s", S_w, k_w e C_S. Direct numerical solution to these equations can be obtained by taking u and w as primary variables (u-w form).
However, it is also possible to formulate the final equations in terms of u and U ( u-U form).
The advantage of using one set of variables rather than the other is a matter of computational effectiveness.
Solving these equations for non-linear dynamic problems can be very expensive. Therefore, under certain conditions, an approximation is useful and indeed more economical for the practical use.