Under either isothermal or nonisothermal conditions, the equations involved in the simulation of FIC are strongly coupled and highly nonlinear. When considering the various equations and their boundary conditions, we can identify possible sources of nonlinearities.

In terms of boundary conditions, the most probable source of nonlinearity originates from the inlet flow rate and from the take-up velocity or force for the simulation of FIC in fiber spinning. Here, you can select appropriate evolution schemes, such as increasing ramps. Throughout the calculation, the increasing flow rate will lead to an increase of other nonlinearities, such as stress development, convection, and dissipation.

The flow rate should not vanish in the simulation of a steady free surface flow. In terms of flow and FIC governing equations, nonlinearities originates from the values of time constants (, , ). Appropriate evolution schemes with increasing functions should be selected. Nonlinearities may also originate from the temperature dependence of these parameters.

Appropriate evolution schemes with increasing functions can be invoked for the parameter in Equation 12–7 and f in Equation 12–14. It is also advised to apply an evolution scheme on the parameter appearing in Equation 12–13, to bound the development of the degree of transformation x, especially when is small.