Least Sqaure Method for Sum of the Functions Satysfying the Differential Equations with Polynomial Coefficients

Abstract

We propose a linear algorithm for determining two function parameters by their linear combination. These functions must satisfy the first order differential equations with polynomial coefficients and our parameters are the coefficients of these polynomials. The algorithm consists of sequential solution by least squares method of two linear problems - first, differential equation polynomial coefficients determining for linear combination of two given functions and second - determining functions parameters by these polynomial coefficients. Numerical modeling carried by this scheme gives an good accordance under weak normal noise (with dispersion (<5%)).