Archive:: American Journal of Applied Mathematics:: Science Publishing Group

Volume 13, Issue 3, June 2025

Research Article
An Efficient A-Stable Linear Multistep Hybrid Block Method for Solving Fifth-Order Initial Value Problems in Ordinary Differential Equations

Duromola Monday Kolawole^*

Issue: Volume 13, Issue 3, June 2025

Pages: 174-193

Received: 9 April 2025

Accepted: 23 April 2025

Published: 29 May 2025

DOI: 10.11648/j.ajam.20251303.11

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Abstract: Furthering research on linear multistep hybrid block methods is essential to enhance accuracy, stability, and efficiency in solving ordinary differential equations, enabling advanced modelling of complex systems across science and engineering for better predictive analysis and real-world applications. In this study, an efficient linear multistep hy... Show More

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Research Article
Mathematical Modelling and Analytical Expressions for Steady-state Concentrations of Non-linear Glucose-responsive Composite Membranes for Closed-loop Insulin Delivery: Akbari-Ganji and Differential Transform Methods

Ranjani Kesavan, Swaminathan Rajagopal, Karpagavalli Ramasamy^*

Issue: Volume 13, Issue 3, June 2025

Pages: 194-204

Received: 15 May 2025

Accepted: 29 May 2025

Published: 11 June 2025

DOI: 10.11648/j.ajam.20251303.12

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Abstract: The dynamic mechanism comprising an enzymatic reaction and the diffusion of reactants and products inside a glucose-sensitive composite membrane is described using a mathematical model created by Abdekhodaie and Wu. A set of non-linear steady-state reaction-diffusion equations is presented in this theoretical model. These equations have been meticu... Show More

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Research Article
Conventional Finite Volumes for Flow Problems in Porous Media Involving Discontinuous Permeability: Convergence Rate Analysis of Cellwise-constant and Linear-spline Solutions

Abdou Njifenjou^*, Clement Obaker Nzonda Noussi, Moussa Sali

Issue: Volume 13, Issue 3, June 2025

Pages: 205-224

Received: 10 April 2025

Accepted: 1 June 2025

Published: 13 June 2025

DOI: 10.11648/j.ajam.20251303.13

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Abstract: This work develops mathematical aspects of Conventional Finite Volume schemes for flow problems in porous media governed by discontinuous absolute permeability. Focusing on incompressible one-phase flow problems in heterogeneous porous media, a particular attention is put on the homogenized absolute permeability involved in the discrete Darcy veloc... Show More

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