Application of the differential transformation method to a nonlinear conservative system. (English) Zbl 1134.65353
Summary: This paper adopts the differential transformation method to solve the free vibrations of a conservative oscillator with inertia and static cubic non-linearities. The concept of differential transformation is briefly introduced, and is then employed to derive a set of difference equations for the free vibration oscillator problem. Parametric studies on the effects of the time response are presented. The results obtained from the differential transformation method are then compared with those from the Runge-Kutta method in order to verify the accuracy of the proposed method. It is shown that excellent agreement exists between the two sets of results.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
References:
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