The investigation of the transient regimes in the nonlinear systems by the generalized classical method

TLDR: In this paper, the generalized classical method (GCM) is used for solving linear and nonlinear differential equations. And the solution of the nonlinear transient regimes in the physical processes can be written as functional series with unknown coefficients.

Abstract: This paper presents the use of the generalized classical method (GCM) for solving linear and nonlinear differential equations. This method is based on the differential transformation (DT) technique. In the GCM, the solution of the nonlinear transient regimes in the physical processes can be written as a functional series with unknown coefficients. The series can be chosen to satisfy the initial and boundary conditions which represent the properties of the physical process. The unknown coefficients of the series are determined from the differential transformation of the nonlinear differential equation of the system. Therefore, the approximate solution of the nonlinear differential equation can be obtained as a closed-form series.