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

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Modification of Picard's Iterative Method for the Solution of Fractional Differential Equations B, Bivan J.; Aminu, Barde; O, Okai J.; G, Madaki A.; Cornelius, Michael; G, Thomas J.; N, Yohanna
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.v3i2.5314

Abstract

A robust algorithm is introduced in the development of the Modified Picard’s Iterative Method (MPIM) to effectively address both linear and nonlinear Fractional Differential Equation (FDE) and other types of 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.
An Enhanced Variational Iteration Method for Solving Ordinary and Partial Differential Equations Hassan, Araga; Adamu, M. Y.; Madaki, A. G.; Nehemiah, Yohanna; Cornelius, Michael; Nasir, U. M.
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.v3i2.5317

Abstract

The Variational Iteration Method (VIM) has proven to be a powerful technique for solving both ordinary and partial differential equations. However, its reliance on Lagrange multipliers for each type of equation has posed significant limitations, complicating its application and reducing its efficiency. This study introduces a Modified Variational Iteration Method (MVIM) that eliminates the need for Lagrange multipliers, addressing these challenges. The MVIM reformulates the correctional functional, simplifying the solution process and enhancing computational efficiency. The method is applied to both linear and nonlinear ordinary and partial differential equations, demonstrating its ability to provide accurate and fast-converging solutions. Numerical examples show that the MVIM outperforms traditional VIM in terms of computational time and convergence speed, and compares favourably with other methods such as the Adomian Decomposition Method (ADM) and New Iteration Method (NIM). The results highlight the potential of MVIM as a versatile and efficient tool for solving complex differential equations in a variety of scientific and engineering applications.
A Semi-Analytical Method for Nonlinear System of Delay Differential Equation via Modified He’s Polynomial Nehemiah, Yohanna; Barde, Aminu; Madaki, A.; 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.v3i2.5319

Abstract

In this work, a simple technique based on the combination of sumudu transform and variational iteration method via Modified He’s polynomial is introduced to solve systems of non-linear delay differential equations. The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, the modified He’s polynomial takes care of the nonlinear terms and hence, making the method less stressful in terms of computations. Also, this technique reduces the complexity of calculating Lagrange’s multiplier values which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.
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.
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.
Co-Authors Abichele, Ogboche Adamu, M. M. Aminu, Barde B, Bivan J. Barde, Aminu D, Ibrahim M. G, Madaki A. G, Thomas J. Hassan, Araga Jeremiah, Adejoh M. Y. Adamu Madaki, A. Madaki, A. G. Mshelia, I. B. N, Yohanna Nasir, U. M. Nehemiah, Yohanna O, Okai J.