A Spline Least Squares Method for Numerical Parameter Estimation in Differential Equations

In this paper, we describe a straightforward least squares approach to the problem of finding numerical values for parameters occurring in differential equations so that the solution best fits some observed data. The method consists of first fitting the given data by least squares using cubic spline functions with knots chosen interactively, and then finding the paramters by least squares solution of the differential equation sampled at a set of points. We illustrate the method by four problems from chemical and biological modeling.