A least squares method for sums of functions satisfying the differential equations with polynomial coefficients

We propose a linear algorithm for determining the parameters of two functions on the basis of their linear combination. These functions must satisfy first-order differential equations with polynomial coefficients, whereas the parameters to be found are the coefficients of these polynomials. The algorithm is based on the least squares method and consists of sequential solution of the following two linear problems: determining the coefficients of polynomial terms in the differential equation satisfied by a linear combination of two given functions and determining the function parameters with the use of these polynomial coefficients. Numerical results obtained according to the above scheme confirm good performance of our method under weak normal noise (with dispersion less than 3 per cent)