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All Journal African Multidisciplinary Journal of Sciences and Artificial Intelligence
Nura Hashim
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology

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A Novel Computational Framework for Nonlinear Differential Equations Employing the Modified Laplace Adomian Polynomial Method Salisu Lukunti; Umar Mujahid Aliyu; Abubakar Assidiq Hussaini; Imafidor Hassan Ibrahim; Mohammed Abubakar Kolo; Sulaiman Ahmad; Nura Hashim; Mohammed Yusuf Marafa; Isa Yahaya
African Multidisciplinary Journal of Sciences and Artificial Intelligence Vol 3 No 1 (2026): African Multidisciplinary Journal of Sciences and Artificial Intelligence
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/amjsai.v3i1.9097

Abstract

Nonlinear differential equations pose significant challenges for conventional analytical and numerical techniques, particularly in efficiently handling complex nonlinear terms while maintaining solution accuracy and stability. This paper presents a novel computational framework for solving such equations using the Modified Laplace–Adomian Polynomial Method (LAPM), which integrates the Laplace transform with an enhanced form of the Adomian Decomposition Method. In the proposed approach, nonlinear terms are systematically decomposed into rapidly convergent Adomian polynomials, simplifying the solution process and reducing computational complexity without compromising precision. The performance of LAPM is evaluated using several benchmark nonlinear and linear differential equations, where it exhibits superior convergence speed, accuracy, and stability when compared with traditional methods. These results demonstrate that the Modified Laplace–Adomian Polynomial Method is a reliable and efficient tool for addressing a wide class of nonlinear differential equations in applied mathematics, physics, and engineering, and contributes to the growing repertoire of semi-analytical techniques for nonlinear problem solving.
A Theoretical Exploration of Paraletrix Calculus as an Extension of Rhotrix Mathematics Isa Yahaya; Salisu Lukunti; Umar Mujahid Aliyu; Imafidor Hassan Ibrahim; Mohammed Abubakar Kolo; Sulaiman Ahmad; Nura Hashim; Mohammed Yusuf Marafa
African Multidisciplinary Journal of Sciences and Artificial Intelligence Vol 3 No 1 (2026): African Multidisciplinary Journal of Sciences and Artificial Intelligence
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/amjsai.v3i1.9100

Abstract

This paper, titled A Theoretical Exploration of Paraletrix Calculus as an Extension of Rhotrix Mathematics, builds upon earlier studies in generalized matrix theory by extending the structural and operational framework of non-standard matrix-like objects. Atanassov and Shannon [1] first introduced matrix-tertions and matrix-ngittrets as entities that interpolate between 2-dimensional vectors and 2×2 matrices, thereby enriching the conceptual landscape of generalized matrices. Ajibade [2] subsequently advanced the field by proposing thotrices as intermediates between 2×2 and 3×3 matrices, while further developments in rhotrix theory have established various multiplication techniques, such as heart-oriented and row–column multiplications—and yielded several important results. Recognizing the diversity of both rectangular and square matrices, the paraletrix structure was formulated as a generalization of the thotrix, allowing unequal numbers of rows and columns and thus providing a more flexible algebraic setting. This study extends the mathematical framework by introducing differentiation and integration within paraletrix calculus, defining these operations for paraletrix-valued functions with respect to an independent variable. In doing so, it lays the groundwork for a coherent calculus on paraletrices as a theoretical extension of rhotrix mathematics and generalized matrix theory.
Co-Authors Abubakar Assidiq Hussaini Imafidor Hassan Ibrahim Isa Yahaya Mohammed Abubakar Kolo Mohammed Yusuf Marafa Salisu Lukunti Sulaiman Ahmad Umar Mujahid Aliyu