Abstract
An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.
Highlights
Function approximation on a fixed interval by means of an initial value problem of an ordinary differential equation with unknown coefficients and unknown initial values as presented by M Shatalov, I
Several other parameter estimation methods are presented in literature, for instance the stochastic models; the Bayesion approach, the Monte Carlo technique, the numerical method with combined Adomain/Alienor approach, the differential evolution (DE) and the hybrid Taguchi-differential evolution algorithm
Tion, we present the analysis for problems from Biology and Ecology
Summary
Function approximation on a fixed interval by means of an initial value problem of an ordinary differential equation with unknown coefficients and unknown initial values as presented by M Shatalov, I. In their paper al method to determine both the unknown coefficients and initial values of a dynamic system by minimizing a certain goal function is presented. The unknown parameters and initial values can be obtained using the method of least squares. The proposed method gives parameter estimates that have a percentage relative error that is mostly less than 0.4% for artificially generated data and parameters that are in the expected range for real data.
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