Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations

• Autorzy: Abdulazeez Sadeq Taha , Modanli Mahmut , Husien Ahmad Muhamad

Identyfikatory

DOI

10.17512/jamcm.2022.4.01

• Języki publikacji: EN

Abstrakty

EN

The numerical solutions to the nonlinear pseudo-hyperbolic partial differentia equation with nonlocal conditions are presented in this study. This equation is solved using the homotopy analysis technique (HAM) and the variational iteration method (VIM). Both strategies are compared and contrasted in terms of approximate and accurate solutions. The results show that the HAM technique is more appropriate, effective, and close to the exact solution than the VIM method. Finally, the graphical representations of the obtained results are given.

Słowa kluczowe

EN

nonlinear pseudo-hyperbolic partial differential equation; homotopy analysis method; variational iteration method; approximate solution

PL

nieliniowe pseudohiperboliczne równanie różniczkowe cząstkowe; homotopijna metoda analizy; metoda iteracji wariacyjnych; rozwiązanie przybliżone

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2022
• Tom: Vol. 21, nr 4
• Strony: 5--15
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Abdulazeez Sadeq Taha

• Department of Mathematics, College of Basic Education, University of Duhok Duhok, Iraq
• Department of Computer Science, College of Science, Nawroz University Duhok, Iraq

autor

Modanli Mahmut

• Department of Mathematics, Faculty of Arts and Sciences, Harran University Sanliurfa, Turkey

autor

Husien Ahmad Muhamad

• Department of Mathematics, College of Science, University of Duhok Duhok, Iraq

Bibliografia

• [1] Lu, T.T., & Zheng, W.Q. (2021). Adomian decomposition method for first order PDEs with unprescribed data. Alexandria Engineering Journal, 60(2), 2563-2572.
• [2] Altaie, S.A., Jameel, A.F., & Saaban, A. (2019). Homotopy perturbation method approximate analytical solution of fuzzy partial differential equation. IAENG International Journal of Applied Mathematics, 49(1), 22-28.
• [3] Nisar, K.S., Ilhan, O.A., Abdulazeez, S.T., Manafian, J., Mohammed, S.A., & Osman, M.S. (2021). Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method. Results in Physics, 21, 103769.
• [4] Ziane, D., & Cherif, M.H. (2022). The homotopy analysis rangaig transform method for nonlinear partial differential equations. Journal of Applied Mathematics and Computational Mechanics, 21(2), 111-122.
• [5] Modanli, M., & Akgül, A. (2018). On solutions to the second-order partial differential equations by two accurate methods. Numerical Methods for Partial Differential Equations, 34(5), 1678-1692.
• [6] Abdulazeez, S.T., & Modanli, M. (2022). Solutions of fractional order pseudo-hyperbolic telegraph partial differential equations using finite difference method. Alexandria Engineering Journal, 61(12), 12443-12451.
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• [8] Modanli, M., Abdulazeez, S.T., & Husien, A.M. (2021). A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions. Numerical Methods for Partial Differential Equations, 37(3), 2235-2243.
• [9] Wang, J., Liu, Y., & Li, H. (2013). A new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic wave equations. International Journal of Mathematical and Computational Sciences, 7(8), 1342-1345.
• [10] Abbas, Z.M.A. (2014). Homotopy analysis method for solving non-linear various problem of partial differential equations. Mathematical Theory and Modeling, 4(14), 113-126.
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• [14] Fedotov, I., Shatalov, M., & Marais, J. (2016). Hyperbolic and pseudo-hyperbolic equations in the theory of vibration. Acta Mechanica, 227(11), 3315-3324.
• [15] Ashyralyev, A., & Köksal, M.E. (2008). A numerical solution of wave equation arising in non-homogeneous cylindrical shells. Turkish Journal of Mathematics, 32(4), 409-427.
• [16] Koksal, M.E. (2011). Recent developments on operator-difference schemes for solving nonlocal BVPs for the wave equation. Discrete Dynamics in Nature and Society, 2011.
• [17] Yokus, A., Durur, H., & Ahmad, H. (2020). Hyperbolic type solutions for the couple Boiti-Leon-Pempinelli system. Facta Universitatis, Series: Mathematics and Informatics, 35(2), 523-531.
• [18] Merad, A., Bouziani, A., & Araci, S. (2015). Existence and uniqueness for a solution of pseudo-hyperbolic equation with nonlocal boundary condition. Applied Mathematics and Information Science, 9(4), 1855-1861.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).