ANALYTICAL SOLUTION OF MODIFIED FORCED VAN DER POL VIBRATION EQUATION USING MODIFIED HARMONIC BALANCE METHOD

M. Wali  Ullah; M. Alhaz  Uddin; M. Saifur  Rahman

doi:10.53808/KUS.2022.ICSTEM4IR.0180-se

Authors

M. Wali Ullah Department of Computer Science & Engineering, Northern University of Business and Technology, Khulna, Bangladesh
M. Alhaz Uddin Department of Mathematics, Khulna University of Engineering & Technology, Khulna-9203, Bangladesh
M. Saifur Rahman Department of Mathematics, Rajshahi University of Engineering & Technology, Rajshahi-6204, Bangladesh

DOI:

https://doi.org/10.53808/KUS.2022.ICSTEM4IR.0180-se

Keywords:

Harmonic balance method, modified Van der Pol Equation, damped oscillators, forcing term.

Abstract

For obtaining analytical solutions to the modified forced Van der Pol equation, the modified harmonic balance method has been developed. In classical harmonic balance method, the numerical procedure is used for solving a set of nonlinear algebraic equations. But it requires laborious computational attempt and accurate primary guesses values which makes it very hard-working to calculate. According to our method, a set of nonlinear algebraic equations has been converted to a set of linear algebraic equations by using a nonlinear one instead of a set. As a result, it reduces the massive computational work. This method provides not only better results than the existing harmonic balance method but also provides very close solutions to the corresponding numerical results. It is noticeable that there is substantial similarity between the approximate and the numerical results attained by the fourth order Runge-Kutta method. Moreover, the method is facile and straightforward. This technique may play great role to handle strongly nonlinear damped systems with external forces.

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