The solution, given the vector k, of the following nonlinear system of equations is the vector u that satisfies this equation:

A simulation is a set of solutions u for a specific sequence of vectors k .
Model simulation can be performed to do the following:
check how well the model predicts the actual values over the historical period
investigate the sensitivity of the solution to changes in the input values or parameters
examine the dynamic characteristics of the model
check the stability of the simultaneous solution
estimate the statistical distribution of the predicted values of the nonlinear model using Monte Carlo methods
By combining the various solution modes with different input data sets, model simulation can answer many different questions about the model. This section presents details of model simulation and solution.