Estimation of parameters in differential equations

In this section we deal with estimating the parameters p in the dynamical model of the form (5.37). As we noticed, methods of Chapter 3 directly apply to this problem only if the solution of the differential equation is available in analytical form. Otherwise one can follow the same algorithms, but solving differential equations numerically whenever the computed responses are needed. The partial derivations required by the Gauss - Newton type algorithms can be obtained by solving the sensitivity equations. While this indirect method is 

The direct integral approach to parameter estimation we will discuss here applies only with all variables y, y2 observed, but then it offers 

Let S (t) denote the ny-vector of natural cubic splines interpolating the 

The Jacobian matrix defined in (3.41) can be easily computed by the same interpolation technique. The idea is to differentiate (3.60) with respect to the parameters changing the order of differentiation and spline integration. 

Completing the procedure we obtain only the approximation (5.60) of the solution of the differential equations (5.37). To see the real goodness-of-fit we must solve the differential equations (5.37) numerically 

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M75 Estimation of parameters in differential equations by direct integral method extension of the Himmelblau-Jones-Bischoff method 7S00 8040... 

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