1
Department of fundamental sciences, Higher Institute for Applied Sciences and Technology, Aleppo, Syria
(george.toma@hiast.edu.sy)
2
Department of mathematics, Faculty of Science, Aleppo University, Aleppo, Syria
(fhmath@yahoo.com)
3
Department of mathematics, Faculty of Science, Aleppo University, Aleppo, Syria
(taaaqimath@gmail.com)
Abstract :
In this paper, an analytical method (Homotopy perturbation method HPM) is used for solving the initial value problem represented by a neutrosophic nonlinear Van der Pol oscillator equation (N-VDP) arising in applied dynamics using the thick function. We find the solutions of the (N-VDP) equation by HPM and then compare the numerical results with fourth order Runge-Kutta method (RK4). The results showed that the HPM lead to accurate and efficient results. Furthermore, these results of the HPM scheme and RK4 are implemented in Matlab.
Keywords :
Neutrosophic Van der pol oscillator , Neutrosophic thick function , Homotopy perturbation method , Nonlinear initial value problem , Fourth Order Runge-Kutta , Approximate solution.
References :
[1] Zadeh. L. A. Fuzzy Sets. Inform. Control 8 (1965).
[2] Atanassov .k, Intuitionistic fuzzy sets. In V. Sgurev, ed., ITKRS Session, Sofia, June 1983, Central Sci. and Techn. Library, Bulg. Academy of Sciences, (1984).
[3] Smarandache F. Neutrosophic Precalculus and Neutrosophic Calculus, University of New Mexico, 705 Gurley Ave. Gallup, NM 87301, USA, 2015.
[4] Smarandache F. Neutrosophic Measure and Neutrosophic Integral, In Neutrosophic Sets and Systems, 3 – 7, Vol. 1, 2013.
[5] A. A Salama, Smarandache F. Kroumov, Neutrosophic Closed Set and Continuous Functions, in Neutrosophic Sets and Systems, Vol.4, 4- 8, 2014.
[6] A. A Salama; I. M Hanafy; Hewayda Elghawalby Dabash M.S, Neutrosophic Crisp Closed RRegion and Neutrosophic Crisp Continuous Functions, New Trends in Neutrosophic Theory and Applications.
[7] A. A Salama. Basic Structure of Some Classes of Neutrosophic Crisp Nearly Open Sets and Possible Application to GIS Topology. Neutrosophic Sets and Systems, Vol. 7, 18-22, (2015).
[8] M. Abdel-Basset; E. Mai. Mohamed; C. Francisco; H. Z. Abd EL-Nasser. "Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases" Artificial Intelligence in Medicine Vol. 101, 101735, (2019).
[9] M. Abdel-Basset; E. Mohamed; G. Abdullah; G. Gunasekaran; L. Hooang Viet." A novel group decision making model based on neutrosophic sets for heart disease diagnosis" Multimedia Tools and Applications, 1-26, (2019).
[10] Aslam, M., Khan, N. and AL-Marshadi, A. H. Design of Variable Sampling Plan for Pareto distribution Using Neutrosophic Statistical Interval Method, Symmetry, 11 (1), 80, (2019).
[11] Shanmugam. G, Palanikumar. M, Arulmozhi. K, Aiyared. I, Said. B Al- Tahan, Agriculture Production Decision Making using Generalized q-Rung Neutrosophic Soft Set Method,International Journal of Neutrosophic Science, Volume 19, Issue 1, PP: 166-176, (2022).
[12] Murtadha. A, Qays. I, Ali. M, Said. B,On Neutrosophic Crisp Generalized Alpha Generalized Closed Sets, International Journal of Neutrosophic Science, Volume 19, Issue 1, PP: 107-115, (2022).
[13] Sonali. P, Ajay. S, Said. B, Review of Generalized Neutrosophic Soft Set in Solving Multiple Expert Decision Making Problems, International Journal of Neutrosophic Science, Volume 19, Issue 1, PP: 48-59, (2022).
[14] George. A. Toma, Exact Solution for Neutrosophic system of Ordinary Differential Equations by Neutrosophic Thick Function Using Laplace Transform, International Journal of Neutrosophic Science, Volume 19, Issue 1, PP: 212-216, (2022).
[15] Madeleine Al- Tahan, Some Results on Single Valued Neutrosophic (Weak) Polygroups, International Journal of Neutrosophic Science, Volume 2, Issue 1, PP: 38-46, (2020).
[16] Malath F. Alaswad, A Study of the Integration of Neutrosophic Thick Functions, International Journal of Neutrosophic Science (IJNS), pp. 97-105, (2020).
[17] Malath F. Alaswad, A Study of Neutrosophic Differential Equation by Using a Neutrosophic Thick, Neutrosophic Knowledge, Vol. 1, (2020).
[18] Kumar, M. and P. Varshney. Numerical Simulation of Van der Pol Equation Using Multiple Scales Modified Lindstedt-Poincare Method. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. Springer, (2020).
[19] Darbyshire, J.H.M. On the numerical solution of the van der pol equation, 2015, Master of Mathematics, the open university, (2015).
[20] J.H. He, Some asymptotic methods for strongly nonlinear equation, Int. J. Nod. Phys., 20, pp. 1144-1199, (2006).
[21] J. H. He, Homotopy perturbation method for solving boundary value problems, Phys. Lett. A, 350, pp. 87-88, (2006).
| Style | # |
|---|---|
| MLA | George A. Toma, Fahed Farhood, Taqi A. Alkhatib. "Approximate Solution of a Neutrosophic Nonlinear Van der Pol Oscillator Problem by Semi Analytical Method Using Thick Function." Full Length Article, Vol. 6, No. 1, 2023 ,PP. 14-20 (Doi : https://doi.org/10.54216/JNFS.060102) |
| APA | George A. Toma, Fahed Farhood, Taqi A. Alkhatib. (2023). Approximate Solution of a Neutrosophic Nonlinear Van der Pol Oscillator Problem by Semi Analytical Method Using Thick Function. Journal of Full Length Article, 6 ( 1 ), 14-20 (Doi : https://doi.org/10.54216/JNFS.060102) |
| Chicago | George A. Toma, Fahed Farhood, Taqi A. Alkhatib. "Approximate Solution of a Neutrosophic Nonlinear Van der Pol Oscillator Problem by Semi Analytical Method Using Thick Function." Journal of Full Length Article, 6 no. 1 (2023): 14-20 (Doi : https://doi.org/10.54216/JNFS.060102) |
| Harvard | George A. Toma, Fahed Farhood, Taqi A. Alkhatib. (2023). Approximate Solution of a Neutrosophic Nonlinear Van der Pol Oscillator Problem by Semi Analytical Method Using Thick Function. Journal of Full Length Article, 6 ( 1 ), 14-20 (Doi : https://doi.org/10.54216/JNFS.060102) |
| Vancouver | George A. Toma, Fahed Farhood, Taqi A. Alkhatib. Approximate Solution of a Neutrosophic Nonlinear Van der Pol Oscillator Problem by Semi Analytical Method Using Thick Function. Journal of Full Length Article, (2023); 6 ( 1 ): 14-20 (Doi : https://doi.org/10.54216/JNFS.060102) |
| IEEE | George A. Toma, Fahed Farhood, Taqi A. Alkhatib, Approximate Solution of a Neutrosophic Nonlinear Van der Pol Oscillator Problem by Semi Analytical Method Using Thick Function, Journal of Full Length Article, Vol. 6 , No. 1 , (2023) : 14-20 (Doi : https://doi.org/10.54216/JNFS.060102) |