Describing Nonlinear RLC Circuit Equation Using Laplace Decomposition Method
DOI:
https://doi.org/10.5890/JAND.2024.09.009Abstract
In this article, the Laplace Adomian Decomposition Method (LADM) is developed to investigate an approximate solution of nonlinear RLC Circuit Equation. This technique involving a permutation between the Laplace transforms (LTM) method with the Adomian decomposition method (ADM). The nonlinear part is involved through an infinite series of Adomian polynomials, and the (LADM) gives an infinite series solution to the equation.References
[1] Varsoliwala, A.C. and Singh, T.R. (2022), Mathematical modeling of atmospheric internal waves phenomenon and its solution by Elzaki Adomian decomposition method, Journal of Ocean Engineering and Science, 7(3), 203-212.
[2] Zephania, C.F.S. and Sil, T. (2022), Modified homotopy perturbation method for damped nonlinear oscillators, Journal of the Physical Society of Japan, 91(10), 104003.
[3] Wang, X., Xu, Q., and Atluri, S.N. (2020), Combination of the variational iteration method and numerical algorithms for nonlinear problems, Applied Mathematical Modelling, 79, 243-259.
[4] Khan, H., Shah, R., Kumam, P., and Arif, M. (2019), Analytical solutions of fractional-order heat and wave equations by the natural transform decomposition method, Entropy, 21(6), 597.
[5] Qayyum, M. and Oscar, I. (2021), Least square homotopy perturbation method for ordinary differential equations, Journal of Mathematics, 2021, 7059194, 1-16
[6] Civelek, C. (2022), Observability, controllability and stability of a nonlinear RLC circuit in form of a Duffing oscillator by means of theoretical mechanical approach, Journal of Electrical Engineering, 73(2), 140-145.
[7] Ates, M. and Laribi, S. (2018), New results on the global asymptotic stability of certain nonlinear RLC circuits, Turkish Journal of Electrical Engineering and Computer Sciences, 26, 434-441.
[8] Thunibat, R.G., Jaradat, E.K., and Khalifeh, J.M. (2021), Solution of non-linear RLC circuit equation using homotopy perturbation transform method, Jordan Journal of Physics, 14(1), 89-100.
[9] Adomain, G. (1988), A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications, 135(2), 501-544.
[10] González-Gaxiola, O. (2017), The Laplace-Adomian decomposition method applied to the Kundu-Eckhaus equation, arXiv preprint arXiv:1704.07730.
[11] Shah, R., Khan, H., Arif, M., and Kumam, P. (2019), Application of Laplace–Adomian decomposition method for the analytical solution of third-order dispersive fractional partial differential equations, Entropy, 21(4), 335.
[12] González-Gaxiola, O. and Biswas, A. (2019), Optical solitons with Radhakrishnan–Kundu–Lakshmanan equation by Laplace–Adomian decomposition method, Optik, 179, 434-442.
[13] Bairwa, R.K. and Singh, K. (2021), Analytical solution of time-fractional Klien-Gordon equation by using Laplace-Adomian decomposition method, Annals of Pure and Applied Mathematics, 24(1), 27-35.
[14] Yousef, H.M. and Ismail, A.M. (2018), Application of the Laplace Adomian decomposition method for solution system of delay differential equations with initial value problem, AIP Conference Proceedings, 1974(1), 020038.
[15] Zhu, H.X., An, H.L., and Chen, Y. (2014), A Laplace decomposition method for nonlinear partial differential equations with nonlinear term of any order, Communications in Theoretical Physics, 61(1), 23.
[16] Hayashi, C. (1964), Nonlinear Oscillation In Physical Systems, McGraw-Hill, Book Company, New York.
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