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All Journal YASIN: Jurnal Pendidikan dan Sosial Budaya Journal of Multidisciplinary Science: MIKAILALSYS
Jeremiah, Adejoh
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Agriculture, Biological Sciences & Forestry Chemical Engineering, Chemistry & Bioengineering Environmental Science Physics Social Sciences Other

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Application of the Kamal-He’s Iterative Method to Klein-Gordons Equations Jeremiah, Adejoh; Adamu, M. Y.; Madaki, A. G.; 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.v3i2.5320

Abstract

This study demonstrates the effectiveness and accuracy of the KHM for solving both linear and nonlinear Klein-Gordon equations. Through graphical comparisons with other methods such as VIM, TAM, and NIM, and error analysis, the results confirm the high precision and reliability of KHM. The approach is shown to be straightforward, easy to implement, and highly efficient for solving linear PDEs. Additionally, KHM provides the exact solution for nonlinear Klein-Gordon equations in a single iteration, highlighting its computational efficiency. Overall, the KHM is proven to be a powerful and reliable tool for solving a wide range of equations in mathematical physics.
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.
Mathematical Model of Transmission Dynamic of Ebola Virus Disease Yohanna, Samuel; Adamu, M. M; Hina, A. D; O, Okai J.; Jeremiah, Adejoh
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.v3i2.5535

Abstract

This study investigates the impact of treatment and vaccination on the transmission dynamics of Ebola virus disease (EVD) within human populations, as well as the effects of environmental factors on vector populations. We formulated a system of ordinary differential equations (ODEs) to model these dynamics and applied the method of linearized stability analysis to solve the equations. The stability analysis revealed that the disease-free equilibrium (DFE) states of the models remain stable when certain parameters—specifically, the treatment rate in the human population and the recovery rate in the vector population—are appropriately adjusted. Numerical simulations demonstrated that achieving a disease-free equilibrium state requires simultaneous treatment and vaccination of the population. The findings highlight the necessity of integrated intervention strategies to effectively control EVD transmission, contributing valuable insights for public health policy and future research on infectious disease management.
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 Abdulmalik, Ibrahim Abichele, Ogboche Adamu, M. M Barde, A. Cornelius, Michael Hina, A. D Kwami, A. M. M. Y. Adamu Madaki, A. G. Mshelia, I. B. O, Okai J. Okai, J. O. Yohanna, Samuel