If a mathematical model is available, then the forward problem can be solved, if all the inputs are known. In the rabbit and fox system modelled by the mathematical model , if the parameters $c0, ..., c3, r0 and f0 are known, an attempt can be made to solve for r(t) and f(t). However, there may not be a closed form expression for the solution to this problem, in which case the solution needs to be approximated by numerical techniques. The computational model or numerical model entails finding approximate solutions to the mathematical model. Similarly, if the populations r(tj) and f(tj) are known at several times tj, j=0,1,...,n, the inverse problem would amount to solving for, or at least approximating, the coefficients c0,...,c3.
It is important to notice at this stage that there are two distinct types of
modelling errors. The first is the difference between the numerical model approximation
and the exact solution to the mathematical model. These are numerical errors.
The other is the difference between the exact solution of the mathematical model
and real world response of the system. These are modelling errors.
A good model is one that is efficient to compute, but has small modelling and
numerical errors in its results.
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