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Ramadan, Mohamed, Mansour, Mariam, El-Shazly, Naglaa, Osheba, Heba. (1405). The double Ramadan group accelerated the Adomian decomposition method for solving nonlinear partial differential equations. سامانه مدیریت نشریات علمی, 14(3), 1320-1336. doi: 10.22034/cmde.2025.65368.3000
Mohamed A. Ramadan; Mariam M. A. Mansour; Naglaa A. El-Shazly; Heba A. Osheba. "The double Ramadan group accelerated the Adomian decomposition method for solving nonlinear partial differential equations". سامانه مدیریت نشریات علمی, 14, 3, 1405, 1320-1336. doi: 10.22034/cmde.2025.65368.3000
Ramadan, Mohamed, Mansour, Mariam, El-Shazly, Naglaa, Osheba, Heba. (1405). 'The double Ramadan group accelerated the Adomian decomposition method for solving nonlinear partial differential equations', سامانه مدیریت نشریات علمی, 14(3), pp. 1320-1336. doi: 10.22034/cmde.2025.65368.3000
Ramadan, Mohamed, Mansour, Mariam, El-Shazly, Naglaa, Osheba, Heba. The double Ramadan group accelerated the Adomian decomposition method for solving nonlinear partial differential equations. سامانه مدیریت نشریات علمی, 1405; 14(3): 1320-1336. doi: 10.22034/cmde.2025.65368.3000

The double Ramadan group accelerated the Adomian decomposition method for solving nonlinear partial differential equations

Computational Methods for Differential Equations
مقاله 19، دوره 14، شماره 3، مهر 2026، صفحه 1320-1336    اصل مقاله (437.1 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.65368.3000
نویسندگان
Mohamed A. Ramadan* 1؛ Mariam M. A. Mansour2؛ Naglaa A. El-Shazly1؛ Heba A. Osheba1
1Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shibin El Kom, Menoufia, Egypt.
2Department of basic science, Modern Academy of Computer Science and Management Technology in Maadi, Maadi, Cairo, Egypt.
چکیده
This paper investigates an advanced method for solving partial differential equations (PDEs) by integrating the Double Ramadan Group Transform (DRGT) with a faster version of the Adomian Decomposition Method (ADM). Initially, the DRGT is applied to transform the PDEs, which simplifies the management of boundary conditions and linear elements. The resulting transformed PDEs are subsequently solved using the enhanced ADM, which is specially tailored to efficiently handle the nonlinear terms that typically make solutions more difficult. The acceleration of the ADM is achieved by utilizing improved decomposition techniques and optimized series expansion methods, leading to significant gains in both the speed of convergence and the accuracy in addressing nonlinearities. The effectiveness of this combined approach is illustrated through several examples involving complex PDEs with challenging nonlinear aspects. The findings demonstrate significant improvements in computational efficiency and solution accuracy, underscoring the potential of this method for solving a wide variety of PDE problems in scientific and engineering applications.
کلیدواژه‌ها
Double Ramadan group transform؛ Adomian decomposition method؛ Double Sumudu Integral transform؛ Double Laplace integral transform؛ Nonlinear partial differential equations؛ Accuracy؛ Efficiency
مراجع
  • [1] K. S. Abdelilah, I. M. Zahra, and S. Rania, Using Double Integral Transform (Laplace-ARA Transform) in Solving Partial Differential Equations, Symmetry, 14(11) (2022).
  • [2] Q. Ali and Z. S. Muhamad, Modeling and Simulation of Phtovoltaic Module with Enhanced Perturb and Observe MPPT Algorithm using MATLAB/ SIMULINK ARPN, Journal of Engineering and Applied Sciences, 11(20) (2016), 12033-12038.
  • [3] A. A. Amjad and A. Anees, The solution of Poisson partial differential Equations via Double Laplace Transform Method, Partial Differential Equations in Applied Mathematics, 18(5) (2021).
  • [4] W. F. Ames, Numerical Methods for Partial Differential Equations, Academic Press, Cambridge, MA, USA, 28(6) (2014).
  • [5] S. Artem, V. Yuri, and N. Vitaliya, Integration of a Low Gas-Saturated Zone in Creating a 3D Model of the Medvezhye Field, Qubahan Academic Journal (QAJ), 3(4) (2023), 476-488.
  • [6] C. Kasumo, On the Approximate Solutions of the Korteweg-de Vries and Viscid Burgers Equations, International Journal of Advances in Applied Mathematics and Mechanics, 8(2) (2020), 64-73.
  • [7] M. J. Churchfield, S. Lee, J. Michalakes, and P. J. Moriarty, A numerical study of the effects of atmospheric and wake turbulence on wind turbine dynamics, Journal of Turbul, 2(5) (2012).
  • [8] R. Courant and D. Hilbert, Methods of Mathematical Physics: Partial Differential Eqs., John Wiley & Sons: Hoboken, NJ, USA, (2008).
  • [9] R. R. Dhunde and G. L. Waghmare, Double Laplace and its Applications, International Journal of Engineering Research and Technology, 2(12) (2013), 1455-1462.
  • [10] M. Tarig Elzaki, Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method, Intech Open Journal, 23(5) (2018).
  • [11] M. T. Elzaki, Double Laplace variational iteration method for solution of nonlinear convolution partial differential Equations, Arch. Des Sci. (ISI Journal), 65(12) (2012), 588-593.
  • [12] H. Eltayeb and A. Kili¸cman, On Double Sumudu Transform and Double Laplace Transform, Malaysian Journal of Mathematical Sciences, 4(1) (2010).
  • [13] S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Courier Corporation, North Chelmsford, MA, USA, 1(1) (1993).
  • [14] G. B. Folland, Introduction to Partial Differential Equations, Princeton University Press: Princeton, NJ, USA, 5(5) (2020).
  • [15] M. Gage, H. Maxwell, C. Venanzio, and J. Ezequiel Martin, Modeling Unmanned Submarine by an Adaptive Control to Follow an Ellipse Path by Considering Disturbances on the System, Journal of Research in Science, Engineering and Technology, 10(4) (2022), 173-187.
  • [16] M. A. Hassan and T. M. Elzaki, Double Elzaki Transform Decomposition Method for Solving Non-Linear Partial Differential Equations, Journal of Applied Mathematics and Physics, 7(8) (2020), 1463-1471.
  • [17] M. Jalil, A. D. Lafta, and L. Mehrdad, 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), 100599.
  • [18] L. Mehrdad, M. Jalil, R. N. Ali, and P. Mohammad, Some new soliton solutions for the nonlinear the fifth-order integrable equations, Computational Methods for Differential Equations, 10(2) (2022), 445-460.
  • [19] D. Mehdi, M. Jalil, and S. Abbas, Solving Nonlinear Fractional Partial Differential Equations Using the Homotopy Analysis Method, Num. Meth. Partial Diff. Eq J., 26 (2010), 448479.
  • [20] O. Mukhtar and M. A. Beshir, Solution of Partial Differential Eq.s with Variables Coefficients Using Double Sumudu Transform, International Journal of Scientific and Research Publications, 6(6) (2016), 2250-3153.
  • [21] E. H. Müller and R. Scheichl, Massively parallel solvers for elliptic partial differential Equations in numerical weather and climate prediction, Quarterly Journal of the Royal Meteorological Society, 16(1) (2014), 2608-2624.
  • [22] H. A. Nawzad, A. M. Sizar, and M. Jalil, Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutions, Partial Differential Equations in Applied Mathematics 9 (2024), 100599.
  • [23] I. G. Petrovsky, Lectures on Partial Differential Equations, Courier Corporation: North Chelmsford, MA, USA, 13(12) (2012).
  • [24] A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer Science & Business Media Springer, Germany, 24(9) (2008).
  • [25] M. A. Ramadan and A. R. Hadhoud, Double Ramadan Group Integral Transform: Definition and Properties with Applications to Partial Differential Equations, Applied Mathematics & Information Sciences An International Journal, 1(3) (2018), 389-396.
  • [26] M. A. Ramadan and A. R. Hadhoud, Ramadan group (RG) transform coupled with Projected Differential Trans- form for Solving Nonlinear Partial Differential Equations, American Journal of Mathematical and Computer Modeling, 6(1) (2016), 103-109.
  • [27] R. M. N. Seyyedeh, T. Nasir, and M. Jalil, Analytical approximations of one-dimensional hyperbolic equation with non-local integral conditions by reduced differential transform method, Computational Methods for Differential Equations, 8(3) (2022), 537-552.
  • [28] J. M. Tchunche and N. S. Mbare, An Application of the double sumudu Transform, Applied Mathematical Sciences, 1(1) (2007), 31-39.
  • [29] F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods, and Applications, American Mathematical Society: Providence, RI, USA, (2010).
  • [30] D. V. Widder, Advanced Calculus, 2nd edition Prentice Hall of India Private Limited, New Delhi, 2005.
  • [31] G. Yanan, C. Xiaoqun, L. Bainian, and G. Mei, Solving Partial Differential Eqs. Using Deep Learning and Physical Constraints, Applied Sciences, 26 (8) (2020).
  • [32] E. Zauderer, Partial Differential Equations of Applied Mathematics, John Wiley & Sons: Hoboken, NJ, USA, 24(10) (2011).
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تعداد مشاهده مقاله: 265
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