Analytical Technique for Solving Van der Pol Oscillator
Md. Zahangir Alam, Ismot Ara Yeasmin, Nazmul Sharif
Abstract
An analytical technique like Differential Transform Method (DTM) is presented to find out the solution of Van der Pol oscillator. In the proposed method, the algebraic relations for determining the unknown coefficients are linear equations and independent of trigonometric functions. To justify the effectiveness and suitability of the method, the obtained solutions are matched to corresponding numerical solutions for several damping conditions. The method proposed herein is straightforward and proficient technique for determining approximate solutions of such kind of nonlinear oscillators.
Conclusion
A methodological approach akin to the Differential Transform method is introduced to tackle the complexity of the extremely nonlinear Van der Pol oscillator. This technique offers simplicity in determining unknown coefficients due to the linear nature of the mathematical relations so formed. Moreover, it yields satisfactory outcomes across various conditions within the range of , demonstrating commendable consistency with numerical solutions. The suggested method stands out as an effective tool for resolving nonlinear problems of this nature.
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