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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 Hindawi Publishing Corporation. 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.