Mathematical Problems in Engineering
Volume 2005 (2005), Issue 5, Pages 503-519
The investigation of the transient regimes in the nonlinear systems by the generalized classical method
1Department of Electrical and Electronic Engineering, Faculty of Engineering, Inönü University, Malatya 44280, Turkey
2Department of Mathematics, Faculty of Arts and Sciences, Inönü University, Malatya 44280, Turkey
Received 10 November 2004; Revised 7 January 2005
Copyright © 2005 T. Abbasov and A. R. Bahadir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
The validity and efficiency of the GCM is shown using some
transient regime problems in the electromechanics processes. The
numerical results obtained by the present method are compared with
the analytical solutions of the equations. It is shown that the
results are found to be in good agreement with each other.