On the Multistage Differential Transformation Method for Analyzing Damping Duffing Oscillator and Its Applications to Plasma Physics

Noufe H. Aljahdaly and S. A. El-Tantawy
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Noufe H. Aljahdaly: Department of Mathematics, Faculty of Sciences and Arts-Rabigh Campus, King Abdulaziz University, Jeddah 21589, Saudi Arabia
S. A. El-Tantawy: Center for Physics Research (CPR), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Al-Baha 65431, Saudi Arabia

Mathematics, 2021, vol. 9, issue 4, 1-12

Abstract: The multistage differential transformation method (MSDTM) is used to find an approximate solution to the forced damping Duffing equation (FDDE). In this paper, we prove that the MSDTM can predict the solution in the long domain as compared to differential transformation method (DTM) and more accurately than the modified differential transformation method (MDTM). In addition, the maximum residual errors for DTM and its modification methods (MSDTM and MDTM) are estimated. As a real application to the obtained solution, we investigate the oscillations in a complex unmagnetized plasma. To do that, the fluid govern equations of plasma species is reduced to the modified Korteweg–de Vries–Burgers (mKdVB) equation. After that, by using a suitable transformation, the mKdVB equation is transformed into the forced damping Duffing equation.

Keywords: multistage differential transformation method; Duffing equation; nonlinear damping oscillations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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