School of Physical Sciences (SPS)

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School of Physical Sciences (SPS)

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Author: search.filters.author.Umaru Mohammed

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    A Novel Seventh-Order Implicit Block Hybrid Nyström-Type Method for Second- Order Boundary Value Problems
    (INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI), 2023-11-05) Joel Olusegun Ajinuhi; Umaru Mohammed; Abdullah Idris Enagi; JIMOH, OMANANYI RAZAQ
    This paper introduces a novel approach for solving second-order nonlinear differential equations, with a primary focus on the Bratu problem, which holds significant importance in diverse scientific areas. Existing methods for solving this problem have limitations, prompting the development of the Block Hybrid Nystrom-Type Method (BHNTM). BHNTM utilizes the Bhaskara points derived, using the Bhaskara cosine approximation formula. The method seeks a numerical solution in the form of a power series polynomial, efficiently determining coefficients. The paper discusses BHNTM's convergence, zero stability, and consistency properties, substantiated through numerical experiments, highlighting its accuracy as a solver for Bratu-type equations. This research contributes to the field of numerical analysis by offering an alternative, effective approach to tackle complex second-order nonlinear differential equations, addressing critical challenges in various scientific domains.
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    Utilizing the Artificial Neural Network Approach for the Resolution of First-Order Ordinary Differential Equations
    (Malaysian Journal of Science and Advanced Technology, 2024-05-28) Khadeejah James Audu; Marshal Benjamin; Umaru Mohammed; Yusuph Amuda Yahaya
    Ordinary Differential Equations (ODEs) play a crucial role in various scientific and professional domains for modeling dynamic systems and their behaviors. While traditional numerical methods are widely used for approximating ODE solutions, they often face challenges with complex or nonlinear systems, leading to high computational costs. This study aims to address these challenges by proposing an artificial neural network (ANN)- based approach for solving first-order ODEs. Through the introduction of the ANN technique and exploration of its practical applications, we conduct numerical experiments on diverse first-order ODEs to evaluate the convergence rate and computational efficiency of the ANN. Our results from comprehensive numerical tests demonstrate the efficacy of the ANN-generated responses, confirming its reliability and potential for various applications in solving first-order ODEs with improved efficiency and accuracy.