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All Journal YASIN: Jurnal Pendidikan dan Sosial Budaya Asian Journal of Science, Technology, Engineering, and Art International Journal of Education, Management, and Technology
Kwami, A. M.
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Arts Computer Science & IT Education Electrical & Electronics Engineering Engineering Materials Science & Nanotechnology Social Sciences Other

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Journal : YASIN: Jurnal Pendidikan dan Sosial Budaya

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Hybrid Yang Transform Method for Fractional Nonlinear Partial Differential Equations Waziri, I. M.; Manjak, N. H.; Kwami, A. M.; Adamu, M. S.; O, Okai J.
YASIN Vol 5 No 3 (2025): JUNI
Publisher : Lembaga Yasin AlSys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/yasin.v5i3.5382

Abstract

This work evaluates the performance of the YTAP and New Iterative Method (NIM) in approximating solutions to both linear and nonlinear partial differential equations (PDEs). Through comparative analysis involving exact solutions, numerical tables, and graphical illustrations, the results demonstrate that both methods are highly effective, with YTAP generally yielding smaller approximation errors. Specifically, in the case of a linear PDE (Example 2), YTAP exhibits superior accuracy, while NIM also performs reliably. For nonlinear PDEs (Example 3), YTAP proves to be a robust and efficient method, successfully generating recursive solutions that closely match the exact results. These findings underscore the reliability of YTAP as a powerful tool for solving a wide range of PDEs.
A One-Step Modified New Iterative Method for Solving Partial Differential Equation Abdulmalik, Ibrahim; Kwami, A. M.; Okai, J. O.; Barde, A.; Abichele, Ogboche; Jeremiah, Adejoh
YASIN Vol 5 No 3 (2025): JUNI
Publisher : Lembaga Yasin AlSys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/yasin.v5i3.5498

Abstract

This study introduces a reliable semi-analytical approach for solving partial differential equations (PDEs) using a Modified New Iterative Method (MNIM). The primary aim is to enhance the efficiency of deriving closed-form solutions through an innovative formulation of an integral operator based on n-fold integration. This approach circumvents the conventional necessity of transforming PDEs into systems of multiple integral equations, thereby streamlining the solution process. The effectiveness of the MNIM is assessed through a series of examples, demonstrating its rapid convergence and superior performance in solving an array of evolution and partial differential equations. The results indicate that the MNIM not only simplifies the solution process but also significantly improves computational efficiency compared to traditional methods. This contribution holds substantial implications for both theoretical advancements in numerical analysis and practical applications across various fields where PDEs are prevalent, thereby facilitating more effective problem-solving strategies in complex systems.
Co-Authors Abdulhameed, M. Abdulmalik, Ibrahim Abichele, Ogboche Adamu, M. M. Adamu, M. S. Barde, A. D, Ibrahim M. Idi, Hamisu Jeremiah, Adejoh Lasisi, Kazeem E. Manjak, N. H. Mshelia, I. B. Muhammad, Muhammad Mubarak N, Nyikyaa M. O, Okai J. Okai, J. O. Waziri, I. M.