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All Journal Mikailalsys Journal of Advanced Engineering International Mikailalsys Journal of Mathematics and Statistics
Akindele, A. A.
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Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering

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Comparative Study of Shifted Chebyshev Polynomials on the Solution of Nonlinear Boundary Value Problems Bepo, A. A.; Oderinu, R. A.; Aderibigbe, A. N.; Adebisi, O.; Akindele, A. A.
Mikailalsys Journal of Advanced Engineering International Vol 2 No 3 (2025): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v2i3.7851

Abstract

The usefulness of orthogonal polynomials has increasingly been extended to the solution of initial and boundary value problems in recent years. Among these, Chebyshev polynomials—classified into four distinct kinds—are widely employed; however, trial functions in numerical schemes have predominantly relied on polynomials of the second kind, with limited attention to the others. This study applies all four kinds of Chebyshev polynomials as trial functions within the collocation method. Shifted forms of each kind of Chebyshev polynomial were used as trial functions and substituted into the governing differential equations. The resulting equations were then evaluated at selected collocation points within the domain, converting the differential equations into systems of linear equations, which were solved simultaneously using Maple 18.0 software. For each kind of Chebyshev polynomial, approximations of sixth, tenth, and twelfth order were constructed, and the corresponding results were compared with available exact solutions and, where exact solutions were not available, with results from other established numerical methods. Three mathematical problems were considered to validate the effectiveness of the four kinds of Chebyshev polynomials in this framework. Residual equations for each kind of polynomial were obtained at different orders, and the associated constants were also determined for each order, thereby providing a systematic assessment of their performance as trial functions in the collocation technique.
Thermo-Magnetic Interaction and Mixed Convection Dynamics of Casson Fluid over a Stretching Surface Bamidele, D. E.; Olumuji, D. O.; Afolabi, M. O.; Olajide, O. A.; Adeyemi, I. T.; Akindele, A. A.
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.v4i1.7852

Abstract

Although thermo-magnetic Casson fluid flow over stretching surfaces has received increasing attention in previous studies, the combined influence of mixed convection, magnetic field strength, and boundary-layer control mechanisms on heat and mass transfer characteristics remains underexplored. This study aims to analyze the interactive effects of magnetic induction, Casson parameter, and convection-related factors on the thermal and velocity profiles of a Casson fluid subjected to thermo-magnetic forces. A quantitative computational approach was employed, in which the governing partial differential equations were transformed into coupled nonlinear ordinary differential equations and solved numerically using MATLAB’s bvp4c solver. The model incorporated key dimensionless parameters, including the magnetic field intensity, Eckert number, Prandtl number, porosity, and inclination angle, to capture mixed convection and thermo-magnetic effects over a porous stretching surface. The findings indicate that increasing magnetic parameter values suppress the velocity profile while enhancing the thermal boundary-layer thickness, reflecting the retarding Lorentz force and associated thermal buildup. Similarly, higher Eckert numbers intensify viscous dissipation, leading to increased temperature fields, whereas larger Prandtl numbers reduce temperature distribution due to diminished thermal diffusivity. These results contribute to the theoretical development of magnetohydrodynamic Casson fluid dynamics and extend understanding of thermo-magnetic interactions in non-Newtonian heat transfer systems. The study concludes that magnetic field modulation and convective parameters play crucial roles in controlling Casson fluid behavior and boundary-layer structure, and recommends that future models incorporate nanoparticle effects and biological considerations to improve prediction accuracy. The implications span applied mathematics, heat transfer modeling, and industrial fluid engineering, with potential applications in cooling systems, polymer processing, and energy devices.
Co-Authors Adebisi, O. Aderibigbe, A. N. Adeyemi, I. T. Afolabi, M. O. Bamidele, D. E. Bepo, A. A. Oderinu, R. A. Olajide, O. A. Olumuji, D. O.