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All Journal Journal of Multidisciplinary Science: MIKAILALSYS Mikailalsys Journal of Mathematics and Statistics
M. Y. Adamu
Mathematical Sciences Programme, Abubakar Tafawa Balewa University
Agriculture, Biological Sciences & Forestry Chemical Engineering, Chemistry & Bioengineering Engineering Environmental Science Mathematics Mechanical Engineering Physics Social Sciences Other

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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.
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.
Multivariate Approaches to Neonatal Assessment of Newborn Babies Garba, B. A.; Baba, A. M.; Adamu, M. Y.
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.v3i3.7453

Abstract

This study examines gender-based differences in neonatal physical characteristics using multivariate statistical techniques. A total of 1,000 newborns (male and female) were sampled from the Federal University Wukari Teaching Hospital, Taraba State, Nigeria. Key anthropometric variables measured included occipito-frontal circumference (OFC), cranial circumference (CC), length of birth (LOB), abdominal circumference (AC), and weight (WT). Due to perfect correlation with other variables, AC was excluded from the multivariate analysis. The objective was to determine whether statistically significant physical differences exist between male and female neonates at birth. The study employed Hotelling’s T² test and profile analysis; however, the assumptions of homogeneity of covariance matrices (tested via Box’s M) and independence (assessed via scatter plots) were violated. To address these issues, a robust non-parametric permutation-based Hotelling’s T² test was conducted, yielding a statistically significant result (p < 0.001), indicating notable gender-based differences in multivariate mean vectors. While the main effect of Feature was highly significant (p < 0.001), revealing differences among OFC, CC, LOB, and WT, the Gender × Feature interaction was non-significant (p > 0.05), suggesting parallel measurement patterns across genders. The study concludes that gender significantly influences neonatal physical traits and that advanced multivariate methods, including Hotelling’s T² and profile analysis, are effective for analyzing high-dimensional neonatal data—even under violations of classical assumptions such as normality and homoscedasticity.
On the Numerical Solutions of Linear and Nonlinear Differential Equations by the Modified Laplace–Adomian Polynomials Method Okai, J. O.; Martha, Iliya; Adamu, M. Y.; Mujahid, U. A.; Sanda, L. N.
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): 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.v4i1.7493

Abstract

This study employs the Laplace–Adomian Polynomial Method (LAPM) to obtain approximate solutions for both linear and nonlinear ordinary differential equations. LAPM integrates the Laplace transform with Adomian polynomials to manage nonlinear terms effectively, avoiding the need for linearization or perturbation techniques. To evaluate the method’s accuracy and computational efficiency, three representative examples were solved, with the results benchmarked against corresponding exact solutions. The numerical outcomes, presented through tables and graphical comparisons, demonstrate that LAPM provides highly accurate approximations with minimal error using only a few series terms. The findings affirm that the method is not only straightforward and computationally efficient but also broadly applicable to various nonlinear problems. Given its robustness and simplicity, LAPM holds promise for extension to more complex systems, including partial differential equations and multi-dimensional models in applied sciences.
Co-Authors Baba, A. M. Cornelius, Michael Garba, B. A. Hassan, Araga Jeremiah, Adejoh Madaki, A. G. Martha, Iliya Mujahid, U. A. Nasir, U. M. Nehemiah, Yohanna O, Okai J. Okai, J. O. Sanda, L. N.