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Symbolic Generation of Adomian Polynomials for Different Nonlinearities by Python | ||
Journal of Chemical and Petroleum Engineering | ||
دوره 58، شماره 1، شهریور 2024، صفحه 103-114 اصل مقاله (327.83 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22059/jchpe.2024.367846.1463 | ||
نویسندگان | ||
Mohsen Noorimohammad؛ Asadollah Houshmand؛ Hooman Fatoorehchi* | ||
School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Iran. | ||
چکیده | ||
The Adomian decomposition method (ADM) is a powerful mathematical technique to find closed-form solutions to nonlinear functional equations including ODEs, PDEs, differential-difference, integral, integro-differential, algebraic, and transcendental equations or systems of such equations. It features a particular infinite series for the representation of nonlinear terms of the equation under study, referred to as the Adomian polynomials. Nevertheless, the computation of such polynomials manually, devoid of any assistance from computational resources, can often be a laborious and protracted endeavor. In this paper, an innovative Python code is proposed, which exploits the SymPy library to perform the involved symbolic calculus operations to generate the Adomian polynomials of any given nonlinear expressions. The use of the code would substantially facilitate the implementation of the ADM to the equations arising in various branches of science and engineering. A number of nonlinear expressions are decomposed to their relevant Adomian polynomials for the sake of demonstration. | ||
کلیدواژهها | ||
Adomian Decomposition Method؛ Adomian Polynomials؛ Differential Equations؛ Nonlinear Equations؛ Python | ||
مراجع | ||
[1] Adomian G, Rach R. On linear and nonlinear integro-differential equations Journal of Mathematical Analysis and Applications. 1986;113(1):199-201. DOI: https://doi.org/10.1016/0022-247X(86)90343-4 [2] Turkyilmazoglu M. A reliable convergent Adomian decomposition method for heat transfer through extended surfaces. International Journal of Numerical Methods for Heat & Fluid Flow. 2018;28(11):2551-2566. DOI: https://doi.org/10.1108/HFF-01-2018-0003 [3] Saifi H, Sari MR, Kezzar M, Ghazvini M, Sharifpur M, Sadeghzadeh M. Heat transfer through converging-diverging channels using Adomian decomposition method. Engineering Applications of Computational Fluid Mechanics. 2020;14(1):1373-1384. DOI: https://doi.org/10.1080/19942060.2020.1830857 [4] Birajdar GA. A new approach for non-linear fractional heat transfer model by Adomian decomposition method. Mathematical Analysis and Computing. 2021; 344:333-343. DOI: https://doi.org/10.1007/978-981-33-4646-8_28 [5] Acharya S, Nayak B, Mishra S, Jena S. Adomian decomposition method for the MHD flow of a viscous fluid with the influence of dissipative heat energy. Heat Transfer. 2020;49(8):4612-4625. DOI: https://doi.org/10.1002/htj.21844 [6] Shamshuddin M, Mishra S, Beg OA, Kadir A. Adomian decomposition method simulation of Von Karman swirling bioconvection nanofluid flow. Journal of Central South University: Science & Technology of Mining and Metallurgy. 2019;26(10):2797-2813. DOI: https://doi.org/10.1007/s11771-019-4214-4 [7] Ostadhossein R, Hoseinzadeh S. The solution of Pennes' bio-heat equation with a convection term and nonlinear specific heat capacity using Adomian decomposition. Journal of Thermal Analysis and Calorimetry. 2022;147(22):12739-12747. DOI: https://doi.org/10.1007/s10973-022-11445-x [8] Yusuf A, Gupa MI, Sayeed NH, Bolarin G. Thermo-diffusion effects of a stagnation point flow in a nanofluid with convection using the Adomian decomposition method. Covenant Journal of Physical and Life Sciences. 2021;9(2). [9] Ajibade AO, Gambo JJ. Adomian decomposition method to magnetohydrodynamics natural convection heat generating/absorbing slip flow through a porous medium. Multidiscipline Modeling in Materials and Structures. 2019;15(3):673-684. DOI: https://doi.org/10.1108/MMMS-08-2018-0153 [10] Putranto YW, Mungkasi S. Adomian decomposition method for solving the population dynamics model of two species. Journal of Physics: Conference Series. 2017;795. DOI: https://doi.org/10.1088/1742-6596/795/1/012045 [11] Yunus AO, Olayiwola MO, Adedokun KA, Adedeji JA, Alaje IA. Mathematical analysis of fractional-order Caputo’s derivative of coronavirus disease model via Laplace Adomian decomposition method. Beni-Suef University Journal of Basic and Applied Sciences. 2022;11(1):144. https://doi.org/10.1186/s43088-022-003269 [12] Ullah A, Ullah A, Ahmad S, Ahmad I, Akgül A. On solutions of fuzzy fractional order complex population dynamical model. Numerical Methods for Partial Differential Equations. 2020:1-21. DOI: https://doi.org/10.1002/num.22654 [13] Lede Y, Mungkasi S. Adomian decomposition method used to solve a SIR epidemic model of dengue fever. In: Proceedings of the 2nd International Conference of Science and Technology for the Internet of Things, ICSTI 2019; September 3rd, 2019; Yogyakarta, Indonesia. [14] Gahgah M, Sari MR, Kezzar M, Eid MR. Duan–Rach modified Adomian decomposition method (DRMA) for viscoelastic fluid flow between nonparallel plane walls. The European Physical Journal Plus. 2020;135(2):250. DOI: https://doi.org/10.1140/epjp/s13360-020- 00250-w [15] Ul Ain Q, Zaheer M. An analysis of an underground water flow using Adomian decomposition method. Water Conservation & Management. 2019;3(1):27-29. DOI: https://doi.org/10.26480/wcm.01.2019.27.29 [16] Mahmood S, Shah R, Khan H, Arif M. Laplace Adomian decomposition method for multidimensional time fractional model of Navier-Stokes equation. Symmetry. 2019;11(2):149. DOI: https://doi.org/10.3390/sym11020149 [17] Momani S, Odibat Z. Analytical solution of a time-fractional Navier–Stokes equation by Adomian decomposition method. Applied Mathematics and Computation. 2006;177(2):488-494. DOI: https://doi.org/10.1016/j.amc.2005.11.025 [18] Fatoorehchi H, Abolghasemi H, Rach R. An accurate explicit form of the Hankinson– Thomas–Phillips correlation for prediction of the natural gas compressibility factor. Journal of Petroleum Science and Engineering. 2014; 117:46-53. DOI: https://doi.org/10.1016/j.petrol.2014.03.004 [19] Fatoorehchi H, Abolghasemi H. Approximating the minimum reflux ratio of multicomponent distillation columns based on the Adomian decomposition method Journal of the Taiwan Institute of Chemical Engineers. 2014;45(3):880-886. DOI: https://doi.org/10.1016/j.jtice.2013.09.032 [20] Fatoorehchi H, Rach R, Sakhaeinia H. Explicit Frost‐Kalkwarf type equations for calculation of vapor pressure of liquids from triple to critical point by the Adomian decomposition method. The Canadian Journal of Chemical Engineering. 2017;95(11):2199- 2208. DOI: https://doi.org/10.1002/cjce.22853 [21] Fatoorehchi H, Abolghasemi H, Rach R. A new parametric algorithm for isothermal flash calculations by the Adomian decomposition of Michaelis–Menten type nonlinearities. Fluid Phase Equilibria. 2015; 395:44-50. DOI: https://doi.org/10.1016/j.fluid.2015.03.024 [22] Fernandes PR. Fast dynamic simulation of distillation columns with local thermodynamic models and Adomian decomposition. IFAC-PapersOnLine. 2021;54(3):383-388. DOI: https://doi.org/10.1016/j.ifacol.2021.08.272 [23] Rach R, Duan J-S, Wazwaz A-M. Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. Journal of Mathematical Chemistry. 2014; 52:255-267. DOI: https://doi.org/10.1007/s10910-013- 0260-6 [24] Fatoorehchi H, Gutman I, Abolghasemi H. Computing graph energy: an alternative approach. Kragujevac Journal of Science. 2014; 36:69-78. DOI: https://doi.org/10.5937/KgJSci1436069F [25] Younker JM. Numerical integration of the chemical rate equations via a discretized Adomian decomposition. Industrial & engineering chemistry research. 2011;50(6):3100- 3109. DOI: https://doi.org/10.1021/ie1008647 [26] Goličnik M. Solution of the extended Michaelis-Menten equation for enzyme kinetics with spontaneous substrate depletion using the Adomian decomposition method. Match Commun Math Comput Chem. 2016;75(3):613-626. [27] Fatoorehchi H, Gutman I, Abolghasemi H. A combined technique for computation of energy-effect of cycles in conjugated molecules. Journal of Mathematical Chemistry. 2015; 53:1113-1125. DOI: https://doi.org/10.1007/s10910-015-0473-y [28] Asma M, Othman WAM, Wong BR, Biswas A. Optical soliton perturbation with quadraticcubic nonlinearity by Adomian decomposition method. Optik. 2018; 164:632-641. DOI: https://doi.org/10.1016/j.ijleo.2018.03.008 [29] Biswas A, Asma M, Alqahtani RT. Optical soliton perturbation with Kerr law nonlinearity by Adomian decomposition method. Optik. 2018; 16:253-270. DOI: https://doi.org/10.1016/j.ijleo.2018.04.025 [30] Rach R, Duan J-S, Wazwaz A-M. On the solution of non-isothermal reaction-diffusion model equations in a spherical catalyst by the modified Adomian method. Chemical Engineering Communications. 2015;202(8):1081-1088. DOI: https://doi.org/10.1080/00986445.2014.900054 [31] Duan J-S, Rach R, Wazwaz A-M. Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method. Journal of Mathematical Chemistry. 2015; 53:1054-1067. DOI: https://doi.org/10.1007/s10910-014-0469-z [32] Jeyabarathi P, Kannan M, Rajendran L. Approximate analytical solutions of biofilm reactor problem in applied biotechnology. Theoretical Foundations of Chemical Engineering. 2021; 55:851-861. DOI: https://doi.org/10.1134/S0040579521050213 [33] Cheng M, Scott K, Sun Y, Wu B. Explicit solution of nonlinear electrochemical models by the decomposition method. Chemical Engineering & Technology. 2002;25(12):1155-1160. DOI: https://doi.org/10.1002/15214125(20021210)25:12<1155::AIDCEAT1155>3.0.CO;2-A [34] Madbouly NM, McGhee DF, Roach GF. Adomian's method for Hammerstein integral equations arising from chemical reactor theory. Applied Mathematics and Computation. 2001;117(2-3):241-249. DOI: https://doi.org/10.1016/S0096-3003(99)00177-0 [35] Biazar J, Pourabd M. A Maple program for computing Adomian polynomials. International Mathematical Forum. 2006;39(1):1919-1924. DOI: https://doi.org/10.13140/RG.2.1.3473.4565 [36] Duan J-S. Recurrence triangle for Adomian polynomials. Applied Mathematics and Computation. 2010;216(4):1235-1241. DOI: https://doi.org/10.1016/j.amc.2010.07.046 [37] Babolian E, Javadi S. New method for calculating Adomian polynomials. Applied Mathematics and Computation. 2004;153(1):253-259. DOI: https://doi.org/10.1016/S0096- 3003(03)00629-5 [38] Biazar J, Babolian E, Kember G, Nouri A, Islam R. An alternate algorithm for computing Adomian polynomials in special cases. Applied Mathematics and Computation. 2003;138(2-3):523-529. DOI: https://doi.org/10.1016/S0096-3003(02)00174-1 [39] Wazwaz A-M. A new algorithm for calculating Adomian polynomials for nonlinear operators. Applied Mathematics and Computation. 2000;111(1):33-51. DOI: https://doi.org/10.1016/S0096-3003(99)00063-6 [40] Fatoorehchi H, Abolghasemi H. On calculation of Adomian polynomials by MATLAB. J Appl Comput Sci Math. 2011; 5:85-88. [41] Abbaoi K, Cherruault Y. Convergence of Adomian's method applied to differential equations. Computers & Mathematics with Applications. 1994;28(5):103-109. DOI: https://doi.org/10.1016/0898-1221(94)00144-8 [42] Babolian E, Biazar J. On the order of convergence of Adomian method. Applied Mathematics and Computation. 2002;130(2-3):383-387. DOI: https://doi.org/10.1016/S0096-3003(01)00103-5 | ||
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