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Perveen, Zahida, Majeed, Afraz Hussain, Refaie Ali, Ahmed. (1405). Exact and iterative solutions for DEs, including Fokker-Planck and Newell-Whitehead-Segel equations, using Shehu transform and HPM. سامانه مدیریت نشریات علمی, 14(1), 201-222. doi: 10.22034/cmde.2024.61746.2683
Zahida Perveen; Afraz Hussain Majeed; Ahmed Refaie Ali. "Exact and iterative solutions for DEs, including Fokker-Planck and Newell-Whitehead-Segel equations, using Shehu transform and HPM". سامانه مدیریت نشریات علمی, 14, 1, 1405, 201-222. doi: 10.22034/cmde.2024.61746.2683
Perveen, Zahida, Majeed, Afraz Hussain, Refaie Ali, Ahmed. (1405). 'Exact and iterative solutions for DEs, including Fokker-Planck and Newell-Whitehead-Segel equations, using Shehu transform and HPM', سامانه مدیریت نشریات علمی, 14(1), pp. 201-222. doi: 10.22034/cmde.2024.61746.2683
Perveen, Zahida, Majeed, Afraz Hussain, Refaie Ali, Ahmed. Exact and iterative solutions for DEs, including Fokker-Planck and Newell-Whitehead-Segel equations, using Shehu transform and HPM. سامانه مدیریت نشریات علمی, 1405; 14(1): 201-222. doi: 10.22034/cmde.2024.61746.2683

Exact and iterative solutions for DEs, including Fokker-Planck and Newell-Whitehead-Segel equations, using Shehu transform and HPM

Computational Methods for Differential Equations
مقاله 14، دوره 14، شماره 1، فروردین 2026، صفحه 201-222    اصل مقاله (498.08 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61746.2683
نویسندگان
Zahida Perveen1؛ Afraz Hussain Majeed2؛ Ahmed Refaie Ali3
1Department of Mathematics, Lahore Garrison University, Lahore, Pakistan.
2School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China.
3Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Menofia, Egypt.
چکیده
This article proposes an iterative method using the Shehu Transform (ST) and the He’s Homotopy Perturbation Method (HPM). Integrating HPM with ST, this study addresses linear and nonlinear instances of equations like Fokker-Planck and Newell-Whitehead-Segel. The method shows reliability and precision through comparisons between exact and approximate results. The Shehu Transform Homotopy Perturbation Method (STHPM) is applied to these equations for the first time, with numerical and graphical comparisons made to HPM and the Elzaki Projected Differential Transform Method (EPDTM). Results demonstrate quick and accurate convergence, offering a robust alternative to traditional numerical methods. Future research explores extending this method to complex systems and real-world applications.
کلیدواژه‌ها
Elzaki projected differential transform (EPDT)؛ He’s homotopy perturbation (HPM)؛ Shehu transformation؛ Newell-Whitehead-Segel؛ Fokker-Planck
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