A family of collocation based methods for parameter estimation in differential equations

Abstract A fully observed state vector is used to estimate the value of an unknown parameter vector in a differential equation model. First the experimental data base is reduced by a least squares technique to a dimension equal to that used in the approximate solution of the model. Next collocation is used to solve the differential equation model and the collocation ordinates are compared with the experimental values using three different methods. One of these methods is previously described in the literature by van den Bosch while the two other methods are based on a different, but statistically reasonable objective function, giving parameters that are close approximations to the maximum likelihood estimates. The numerical operations involved in the three methods are first demonstrated, using a simple example which is worked out in detail. Next the relative merits of the three methods are compared in a computer simulation of three examples. Finally, in a conclusion a word of warning is given on inappropriate use of any of the three methods in situations where simpler alternatives are available.