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All Journal YASIN: Jurnal Pendidikan dan Sosial Budaya Journal of Multidisciplinary Science: MIKAILALSYS International Journal of Education, Management, and Technology
Mshelia, I. B.
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Agriculture, Biological Sciences & Forestry Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Education Electrical & Electronics Engineering Engineering Environmental Science Materials Science & Nanotechnology Physics Social Sciences Other

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Enhancement of the Kamal Transform Method with the He’s Polynomial for Solving Partial Differential Equations (Telegraph Equation) Abichele, Ogboche; Mshelia, I. B.; Madaki, A. G.; Jeremiah, Adejoh; O, Okai J.; Cornelius, Michael
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.v3i2.5321

Abstract

This study proposes a hybrid solution methodology that integrates the Kamal Transform Method (KTM) with He’s Polynomial Method (HPM) for solving nonlinear partial differential equations (PDEs), with a focus on the telegraph equation. The telegraph equation, which models wave propagation and diffusive behaviors, presents significant challenges in terms of nonlinearity, complex boundary conditions, and slow convergence in traditional methods. By combining the transformation power of the Kamal method with the iterative, rapidly converging He’s polynomial method, this research aims to enhance the accuracy, convergence, and computational efficiency of existing solution techniques for PDEs. The proposed hybrid approach is applied to both linear and nonlinear forms of the telegraph equation, demonstrating excellent agreement with exact solutions and offering significant improvements in accuracy, especially in the presence of nonlinearities. Comparative analyses with traditional methods, including Elzaki's transform, show that the Kamal-He’s polynomial method outperforms existing techniques in terms of error reduction. The results highlight the method's potential for broader application in various fields of engineering, physics, and applied sciences, where complex, nonlinear PDEs are commonly encountered.
A Modified Iterative Approach for Solving Linear Fractional-Order Delay Differential Equations D, Ibrahim M.; Adamu, M. M.; Mshelia, I. B.; Cornelius, Michael; Nasir, U. M.; O, Okai J.
YASIN Vol 5 No 2 (2025): APRIL
Publisher : Lembaga Yasin AlSys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/yasin.v5i2.5363

Abstract

This paper explores the application of the Modified New Iterative Method (MNIM) for solving linear fractional-order delay differential equations (FDDEs). The method is assessed through illustrative example, showcasing its effectiveness in producing accurate approximations for linear case, particularly when the fractional order approaches an integer. MNIM demonstrates strong performance in solving equations of integer and near-integer fractional order. However, the accuracy declines as the fractional order moves further from an integer, especially over larger intervals. MNIM remains a powerful and adaptable method for handling a broad spectrum of fractional differential equations involving delays.
A Modified New Iterative Method for Solving Nonlinear Fractional-Order Delay Differential Equations D, Ibrahim M.; Adamu, M. M.; Mshelia, I. B.; Kwami, A. M.; O, Okai J.; N, Nyikyaa M.
International Journal of Education, Management, and Technology Vol 3 No 2 (2025): International Journal of Education, Management, and Technology
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijemt.v3i2.5381

Abstract

This paper explores the application of the Modified New Iterative Method (MNIM) to solve nonlinear fractional-order delay differential equations (NFDDEs). A series of test problems are presented to evaluate the method's performance across various fractional orders. The results indicate that MNIM yields highly accurate approximations, particularly when the fractional order approaches an integer. The method is especially effective for integer-order cases and for fractional orders close to them. However, its accuracy decreases as the fractional order becomes smaller, with noticeable errors emerging over larger domains. MNIM remains a powerful and adaptable approach for solving a broad class of fractional differential equations.
Co-Authors Abichele, Ogboche Adamu, M. M. Cornelius, Michael D, Ibrahim M. Jeremiah, Adejoh Kwami, A. M. Madaki, A. G. N, Nyikyaa M. Nasir, U. M. O, Okai J.