1
Directorate General of Education Rusafa 2, Ministry of Education, Iraq
(Nawar.nh27@gmail.com)
Abstract :
In this paper, we propose a novel combination of the (He) method with (Mohand transform), and this combination is summarized by representing the nonlinear part (or the residue of the operator) with (He) polynomials after applying the Mohand transform. To prove the accuracy of the proposed method, we applied it to several neutrosophic partial differential equations such as neutrosophic version of Helmholtz equation, neutrosophic version of non-linear oscillator, neutrosophic version of Burger's equation, and the neutrosophic version of telegraph equation. The accuracy and effectiveness of the application of the proposed method was verified by comparing the results obtained with other methods using the Maple software package.
Keywords :
neutrosophic partial differential equation; Mohand transform; numerical solution; exact solution
References :
[1] Smarandache, F., " A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy,
Neutrosophic Set, Neutrosophic Probability", American Research Press. Rehoboth, 2003.
[2] Shaher, Salah,, Application of He’s variational iterational method to Helmholtz equation, researchgate,(2006)
[3] Syed Tauseef Mohyud-Din and Muhammad Aslam Noor, Homotopy Perturbation Method for Solving Partial Differential Equations, Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan(2008).
[4] Wu Y and He JH. Homotopy perturbation method for nonlinear oscillators with coordinate-dependent mass. Results Phys 2018; 10: 270–271 2018.
[5] Junfeng Lu and Li Ma, The VIM-Pade´ technique for strongly nonlinear oscillators with cubic and harmonic restoring force. 2019
[6] Bateman, Some recent researches on the motion of fluids, Mon. Wea. Rev., 43 (1915), 163-170.
[7] Mahgoub, M.A.M. and Alshikh, A.A., An application of new transform “Mahgoub Transform” to partial differential equations, Mathematical Theory and Modeling, 7(1), 7-9, 2017.
[8] Hradyesh Kumar Mishra and Atulya K. Nagar, He-Laplace Method for Linear and Nonlinear Partial Differential Equations, 11 June 2012.
[9] 1SalimaA. MohamedZebir, 2.3Mohand M. Abdelrahim Mahgoub, Application of Homotopy Perturbation SolvingBurgers Equations, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319 765X. Volume 17, Issue 1 Ser. I (Jan. – Feb. 2021).
[10] Muhammad Nadeem and Fengquan Li, He–Laplace method for nonlinear vibration systems and nonlinear wave equations, Journal of Low Frequency Noise, Vibration and Active Control 2019.
[11] Syed Tauseef Mohyud-Din, Solving Heat and Wave-like Equations Using He’s Polynomials , Hindawi Publishing Corporation Mathematical Problems in Engineering 2009.
[12] Mahmoud Ismail, Mahmoud Ibrahiem, Multi-Criteria Decision-Making Approach based on Neutrosophic Sets for Evaluating Sustainable Supplier Selection in the Industrial 4.0, Journal of American Journal of Business and Operations Research, Vol. 7 , No. 2 , (2022) : 41-55 (Doi : https://doi.org/10.54216/AJBOR.070204)
[13]Abobala, M., " n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules", International Journal of Neutrosophic Science, 2020.
[14] Gustavo Alvarez Gómez, Corona Gómez Armijos, Ariel Romero Fernández, Asmaa Ahmed, Teaching risk assessment index system using neutrosophic AHP: Data Fusion method, Journal of Fusion: Practice and Applications, Vol. 14 , No. 2 , (2024) : 199-210 (Doi : https://doi.org/10.54216/FPA.140216)
[15]Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, 2021.
[16] Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in Physics, 143-146, Vol. 4, 2013.
[17] Agboola, A.A.A., “On Refined Neutrosophic Algebraic Structures”, Neutrosophic Sets and Systems,Vol.10, pp. 99-101, 2015.
[18] Hatip, A., and Olgun, N., " On Refined Neutrosophic R-Module", International Journal of Neutrosophic Science, Vol. 7, pp.87-96, 2020.
| Style | # |
|---|---|
| MLA | Nawar Hazim Mohammed. "On Developing He Method with Mohand Transform to Find Numerical and Exact Solutions of Some Neutrosophic Partial Differential Equations." International Journal of Neutrosophic Science, Vol. 23, No. 4, 2024 ,PP. 238-243 (Doi : https://doi.org/10.54216/IJNS.230418) |
| APA | Nawar Hazim Mohammed. (2024). On Developing He Method with Mohand Transform to Find Numerical and Exact Solutions of Some Neutrosophic Partial Differential Equations. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 238-243 (Doi : https://doi.org/10.54216/IJNS.230418) |
| Chicago | Nawar Hazim Mohammed. "On Developing He Method with Mohand Transform to Find Numerical and Exact Solutions of Some Neutrosophic Partial Differential Equations." Journal of International Journal of Neutrosophic Science, 23 no. 4 (2024): 238-243 (Doi : https://doi.org/10.54216/IJNS.230418) |
| Harvard | Nawar Hazim Mohammed. (2024). On Developing He Method with Mohand Transform to Find Numerical and Exact Solutions of Some Neutrosophic Partial Differential Equations. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 238-243 (Doi : https://doi.org/10.54216/IJNS.230418) |
| Vancouver | Nawar Hazim Mohammed. On Developing He Method with Mohand Transform to Find Numerical and Exact Solutions of Some Neutrosophic Partial Differential Equations. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 4 ): 238-243 (Doi : https://doi.org/10.54216/IJNS.230418) |
| IEEE | Nawar Hazim Mohammed, On Developing He Method with Mohand Transform to Find Numerical and Exact Solutions of Some Neutrosophic Partial Differential Equations, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 4 , (2024) : 238-243 (Doi : https://doi.org/10.54216/IJNS.230418) |