Galerkin Method and Qualitative Approach for the Investigation and Numerical Analysis of Some Dissipative Nonlinear Physical Systems

Abstract

The mathematical models of the oscillations for the important classes of the nonlinear physical systems with dissipation are considered in the paper. It is impossible to apply the asymptotic analytical methods to construct the solutions in the mathematical models of the dynamical processes in these systems. Consequently the qualitative approach is used, the solution existence and uniqueness is substantiated and estimated. The qualitative methods enable to use the corresponding specified numerical methods for the investigation of the mathematical model and solution construction. Basing on the numerical analysis and the fourth-order Runge-Kutta method there are analyzed some singularities of the dynamical processes in the considered systems classes. The effective combination of the theoretic and numerical approach allows to build the innovative procedure to analyze the mathematical models for the wide class of the nonlinear physical systems applied in the engineering.