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

ID
TR-80-08
Authors
James M. Varah
Publishing date
January 1980
Abstract

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 parameters by least squares solution of the differential equation sampled at a set of points. We illustrate the method by three problems from chemical and biological modelling.