The Discrete Ordinates and the Riccati Equation Methods in thee Estimation of Growth of Solutions of Systems of two Linear first Order Ordinary Dierential Equations

Abstract

The method of comparing the solutions of a system of linear equations with solutions of such a system with piecewise constant coefficients (the discrete ordinates method) and Rtccati equation method is used for estimating solutions of systems of two first order linear equations. Two principal (essentially dierent) cases have been considered, for which some explicit estimates in terms of coefcients of linear systems have been obtained. By examples the obtained results are compared with the results obtained by methods of Liapunov, Yu. S. Bogdanov, T. Wazevski, estimates of solutions by logarithmic norm of S. M. Lozinski and the method of freezing.