Application of the analytical method for solving the chemical kinetics system

Hassan, Inaam Rikan

doi:10.22034/cmde.2024.64302.2910

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,420
تعداد مقالات	17,508
تعداد مشاهده مقاله	56,648,974
تعداد دریافت فایل اصل مقاله	18,794,761

	Application of the analytical method for solving the chemical kinetics system
Computational Methods for Differential Equations
مقاله 12، دوره 13، شماره 4، دی 2025، صفحه 1233-1249 اصل مقاله (381.19 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.64302.2910
نویسنده
Inaam Rikan Hassan^*
University of Information Technology and Communications, (UoITC), Baghdad, Iraq.
چکیده
This work introduces an enhanced $tan(\chi/2)$-expansion method to obtain exact solutions for chemical kinetics systems. This technique works directly with the governing equations of chemical kinetics systems. Our work yields many new fundamental traveling wave solutions that combine periodic functions with soliton-like and other trigonometric shapes. To better illustrate our solutions, we show visual representations by assigning specific values to the arbitrary constants. The improved expansion method successfully obtains kink, singular kink, and multiple soliton solutions. The results demonstrate that the method is effective for real-world applications and physics equations. Graphical visualizations support our findings to show the method's accuracy and reliability. Our suggested method effectively solves nonlinear equations and provides useful results for studying complicated wave behavior across multiple scientific disciplines.
کلیدواژه‌ها
Improved $\tan\left(\Phi(\chi)/2\right) $-expansion method؛ Generalized (G’/G)-expansion method؛ Travelling wave؛ The chemical kinetics system؛ Solitons؛ Kink؛ Periodic and rational solutions

مراجع
[1] M. F. Aghdaei and J. M. Heris, Exact solutions of the couple Boiti-Leon-Pempinelli system by the generalized G′/G-expansion method, J. Math. Ext, 5 (2011), 91-104. [2] A. A. Al-Ansari, M. M. Kharnoob, and M. A. Kadhim, Abaqus Simulation of the Fire’s Impact on Reinforced Concrete Bubble Deck Slabs, E3S Web Conf., 427 (2023), 02001. [3] N. H. Ali, S. A. Mohammed, and J. Manafian, Study on the simplified MCH equation and the combined KdVmKdV equations with solitary wave solutions, Partial Diff. Eq. Appl. Math., 9 (2024), 100599. [4] H. Aminikhah, An analytical approximation to the solution of chemical kinetics system, J. King Saud University Sci., 23 (2011), 167-170. [5] J. C. Butcher, Numerical Methods for Ordinary Differential Equations, John Wiley and Sons, 2003. [6] M. Dehghan and J. Manafian, The solution of the variable coefficients fourth–order parabolic partial differential equations by homotopy perturbation method, Z. Naturforsch, 64(a) (2009), 420-430. [7] M. Dehghan, J. Manafian, and A. Saadatmandi, Solving nonlinear fractional partial differential equations using the homotopy analysis method, Num. Meth. Partial Differential Eq. J., 26 (2010), 448-479. [8] M. Dehghan, J. Manafian, and A. Saadatmandi, The solution of the linear fractional partial differential equations using the homotopy analysis method, Z. Naturforsch, 65(a) (2010), 935-949. [9] M. Dehghan, J. Manafian, and A. Saadatmandi, Application of semi–analytic methods for the Fitzhugh–Nagumo equation, which models the transmission of nerve impulses, Math. Meth. Appl. Sci., 33 (2010), 1384-1398. [10] M. Dehghan, J. M. Heris, and A. Saadatmandi, Application of the Exp-function method for solving a partial differential equation arising in biology and population genetics, Int. J. Num. Meth. Heat Fluid Flow, 21 (2011), 736-753. [11] M. Dehghan, J. M. Heris, and A. Saadatmandi, Analytical treatment of some partial differential equations arising in mathematical physics by using the Exp-function method, Int. J. Modern Phys. B, 25 (2011), 2965-2981. [12] Y. Gu, S. Malmir, J. Manafian, O. A. Ilhan, A. A. Alizadeh, and A. J. Othman, Variety interaction between k-lump and k-kink solutions for the (3+1)-D Burger system by bilinear analysis, Results Phys., 43 (2022), 106032. [13] J. H. He, Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech., 34 (1999), 699-708. [14] J. M. Heris and M. Bagheri, Exact solutions for the modified KdV and the generalized KdV equations via Expfunction method, J. Math. Ext., 4 (2010), 77-98. [15] J. M. Heris and M. Lakestani, Solitary wave and periodic wave solutions for variants of the KdV-Burger and the K(n, n)-Burger equations by the generalized tanh-coth method, Commun. Num. Anal., 2013 (2013), 1-18. [16] J. M. Heris and M. Lakestani, Exact solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system by the analytical methods, Int. Schol. Research Notices, 2014 (2014), 840689. [17] H. Jafari, A. Kadem, and D. Baleanu, Variational iteration method for a fractional-order Brusselator system, Abs. Appl. Anal., 2014 (2014), 496323. [18] M. M. Khader, On the numerical solutions for chemical kinetics system using Picard-Pade’ technique, J. King Saud Univ. Eng. Sci., 25 (2013), 97-103. [19] M. M. Kharnoob, A. I. Hammood, and A. H. J. Hasan, A review: The structures of vibration control devices of Zn and Fe based on memory system alloy, Materials Today: Proc. 42(5) (2021), 3035-3040. [20] M. Lakestani, J. Manafian, A. R. Najafizadeh, and M. Partohaghighi, Some new soliton solutions for the nonlinear the fifth-order integrable equations, Comput. Meth. Diff. Equ., 10(2) (2022), 445-460. [21] J. Manafian and I. Zamanpour, Exact travelling wave solutions of the symmetric regularized long wave (SRLW) using analytical methods, Stat., Optim. Inf. Comput., 2 (2014), 47-55. [22] J. Manafian and M. Lakestani, Application of tan(ϕ/2)-expansion method for solving the Biswas-Milovic equation for Kerr law nonlinearity, Optik, 127(4) (2016), 2040-2054. [23] J. Manafian and M. Lakestani, Optical soliton solutions for the Gerdjikov-Ivanov model via tan(ϕ/2)-expansion method, Optik, 127(20) (2016), 9603-9620. [24] J. Manafian and M. Lakestani, Abundant soliton solutions for the Kundu-Eckhaus equation via tan(ϕ(ξ))expansion method, Optik, 127(14) (2016), 5543-5551. [25] J. Manafian and M. Lakestani, N-lump and interaction solutions of localized waves to the (2+ 1)- dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation, J. Geom. Phys., 150 (2020), 103598. [26] J. Manafian, L. A. Dawood, and M. Lakestani, New solutions to a generalized fifth-order KdV like equation with prime number p = 3 via a generalized bilinear differential operator, Partial Diff. Eq. Appl. Math., 9 (2024), 100600. [27] S. R. Moosavi, N. Taghizadeh, and J. Manafian, Analytical approximations of one-dimensional hyperbolic equation with non-local integral conditions by reduced differential transform method, Comput. Meth. Diff. Equ., 8(3) (2020), 537-552. [28] H. Naher and F. A. Abdullah, New approach of (G’/G)-expansion method and new approach of generalized (G’/G)-expansion method for nonlinear evolution equation, AIP Advan., 3 (2013), 032116. [29] M. G. Sakar and F. Erdogan, The homotopy analysis method for solving the time-fractional Fornberg.Whitham equation and comparison with Adomian’s decomposition method, Appl. Math. Model., 37 (2013), 8876-8885. [30] K. Sherazi, N. Sheikh, M. Anjum, and A. G. Raza, Solar drying experimental research and mathematical modelling of wild mint and peach moisture content, J. Asian Sci. Research, 13(2) (2023), 94-107. [31] X. Wang and L. Zhou, Unveiling the mediating role of self-esteem in the relationship between physical activity and BMI: A structural equation modeling study in adolescents, J. Asian Sci. Research, 14(2) (2024), 208-226. [32] S. Yu, N. Jantharajit, and S. Srikhao, Collaborative inquiry-based instructional model to enhance mathematical analytical thinking and reasoning skills for fourth-grade students, Asian J. Edu. Train., 10(1) (2024), 10-17. [33] M. Zhang, X. Xie, J. Manafian, O. A. Ilhan, and G. Singh, Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation, J. Adv. Res., 38 (2022), 131-142.
آمار تعداد مشاهده مقاله: 136 تعداد دریافت فایل اصل مقاله: 179

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Application of the analytical method for solving the chemical kinetics system