Justification of the averaging method for the boundary value problems on a finite or semi-infinite interval

Authors: Levenshtam V.B., Shubin P.E.

Keywords: normal ODE system; boundary value problems; high frequency; averaging method

Abstract:

We justify the averaging technique for the boundary value problems for the normal ODE systems involving large parameters on a finite or semi-infinite interval.

References:

[1] V. B. LEVENSHTAM, P. E. SHUBIN, Averaging of Evolution System with Boundary Conditions, Ser. A: Appl. Math. Inform. and Mech. 2013. Vol. 5, No 2. P. 61–67. [2] B. P. DEMIDOVICH, Lectures on the mathematical theory of stability, Nauka, Moscow, 1967. [3] S. K. GODUNOV, Ordinary differential equations with constant coefficient, Publishing University of Novosibirsk, Novosibirsk, 1994. [4] Y. L. DALETSKII, M. G. KREIN, Stability of solutions of differential equations in Banach spaces, Nauka, Moscow, 1970. [5] I. B. SIMONENKO, A Justification of the averaging method for abstract parabolic equations, Math. USSR Sb. 10 51., 1970. [6] I. B. SIMONENKO, The averaging method in the theory of nonlinear equations of parabolic type with application to problems of hydrodynamic stability, PRU, Rostov-on-Don, 1989.