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All Journal YASIN: Jurnal Pendidikan dan Sosial Budaya Journal of Multidisciplinary Science: MIKAILALSYS Mikailalsys Journal of Mathematics and Statistics
Waziri, I. M.
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Agriculture, Biological Sciences & Forestry Chemical Engineering, Chemistry & Bioengineering Engineering Environmental Science Mathematics Mechanical Engineering Physics Social Sciences Other

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Enhancing the Daftardar Jafari Method for Solving the Bagley–Torvik Equation through Numerical Approaches Saje, A. A; Kwami, A. M; Madaki, A. G; O, Okai J.; Waziri, I. M.; Hafsat, Yakubu
Journal of Multidisciplinary Science: MIKAILALSYS Vol 3 No 2 (2025): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v3i2.5337

Abstract

A robust algorithm is introduced in the development of the Enhanced Daftardar Jafari Method (DJM) to effectively address both linear and nonlinear Bagley–Torvik equations (BTE) and other fractional order differential equations. The method's efficacy is demonstrated through numerical examples, showcasing its ability to solve these equations without resorting to linearization or small perturbations. The results affirm the method's strength, accuracy, and simplicity in comparison to alternative approaches.
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 Hybrid of Adomian Decomposition Method for the Solution of Logistic Equations Waziri, I. M.; Waziri, Usman; S., Kamfa A.
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6403

Abstract

This study introduces a novel analytical technique that integrates the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) to solve nonlinear differential equations, with particular emphasis on logistic growth models. The proposed hybrid method leverages the recursive decomposition mechanism of ADM alongside the correction functional framework of VIM to improve both the convergence rate and the accuracy of the solutions. To assess its effectiveness, the method is applied to selected cases of the logistic differential equation. The resulting approximate solutions exhibit strong agreement with known exact solutions, demonstrating the method's reliability and potential in addressing complex nonlinear problems in applied mathematics. This approach offers a robust alternative for researchers and practitioners seeking efficient analytical tools for nonlinear modeling.
Co-Authors Adamu, M. S. Hafsat, Yakubu Kwami, A. M Kwami, A. M. Madaki, A. G Manjak, N. H. O, Okai J. S., Kamfa A. Saje, A. A Waziri, Usman