This study aims to develop an efficient and accurate numerical method for solving the boundary layer fluid flow over a stretching sheet using a modified spectral quasilinearization method. The governing partial differential equations (PDEs) for momentum and energy are first transformed into a system of nonlinear ordinary differential equations (ODEs) using similarity transformations. The improvement in the method of solution is realized by numerically solving the flow equations defined over a larger semi-infinite domain [0, ∞) using spectral quasilinearization method embedded on overlapping sub-intervals. This method is better than its counterpart on a single domain as it maintains high accuracy and at the same time results in a sparse differentiation matrix that is easily invertible and saves CPU time. The numerical simulations and solution error analysis were performed using MATLAB version 2018a. Convergence analysis demonstrates exponential error decay, with residual errors reducing from the order of 10−2 to approximately 10−12 within four iterations, confirming the accuracy and efficiency of the numerical scheme. Additionally, the impact of the Prandtl number on thermal boundary layer thickness is examined, revealing sharper temperature gradients for higher Pr values. This method can be adapted to solve other fluid flow problems represented as systems of nonlinear ODEs.
| Published in | American Journal of Applied Mathematics (Volume 13, Issue 4) |
| DOI | 10.11648/j.ajam.20251304.14 |
| Page(s) | 274-281 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Stretching Sheet, Spectral Quasilinearization Method, Overlapping Sub-intervals, Similarity Transformation
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APA Style
Mwakio, M. J., Mutua, S., Habiyaremye, F. (2025). Modified Spectral Quasilinearization Method for Solving Fluid Flow over Stretching Sheet. American Journal of Applied Mathematics, 13(4), 274-281. https://doi.org/10.11648/j.ajam.20251304.14
ACS Style
Mwakio, M. J.; Mutua, S.; Habiyaremye, F. Modified Spectral Quasilinearization Method for Solving Fluid Flow over Stretching Sheet. Am. J. Appl. Math. 2025, 13(4), 274-281. doi: 10.11648/j.ajam.20251304.14
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Download@article{10.11648/j.ajam.20251304.14,
author = {Mwatela James Mwakio and Samuel Mutua and Felicien Habiyaremye},
title = {Modified Spectral Quasilinearization Method for Solving Fluid Flow over Stretching Sheet
},
journal = {American Journal of Applied Mathematics},
volume = {13},
number = {4},
pages = {274-281},
doi = {10.11648/j.ajam.20251304.14},
url = {https://doi.org/10.11648/j.ajam.20251304.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251304.14},
abstract = {This study aims to develop an efficient and accurate numerical method for solving the boundary layer fluid flow over a stretching sheet using a modified spectral quasilinearization method. The governing partial differential equations (PDEs) for momentum and energy are first transformed into a system of nonlinear ordinary differential equations (ODEs) using similarity transformations. The improvement in the method of solution is realized by numerically solving the flow equations defined over a larger semi-infinite domain [0, ∞) using spectral quasilinearization method embedded on overlapping sub-intervals. This method is better than its counterpart on a single domain as it maintains high accuracy and at the same time results in a sparse differentiation matrix that is easily invertible and saves CPU time. The numerical simulations and solution error analysis were performed using MATLAB version 2018a. Convergence analysis demonstrates exponential error decay, with residual errors reducing from the order of 10−2 to approximately 10−12 within four iterations, confirming the accuracy and efficiency of the numerical scheme. Additionally, the impact of the Prandtl number on thermal boundary layer thickness is examined, revealing sharper temperature gradients for higher Pr values. This method can be adapted to solve other fluid flow problems represented as systems of nonlinear ODEs.
},
year = {2025}
}
TY - JOUR T1 - Modified Spectral Quasilinearization Method for Solving Fluid Flow over Stretching Sheet AU - Mwatela James Mwakio AU - Samuel Mutua AU - Felicien Habiyaremye Y1 - 2025/08/05 PY - 2025 N1 - https://doi.org/10.11648/j.ajam.20251304.14 DO - 10.11648/j.ajam.20251304.14 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 274 EP - 281 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20251304.14 AB - This study aims to develop an efficient and accurate numerical method for solving the boundary layer fluid flow over a stretching sheet using a modified spectral quasilinearization method. The governing partial differential equations (PDEs) for momentum and energy are first transformed into a system of nonlinear ordinary differential equations (ODEs) using similarity transformations. The improvement in the method of solution is realized by numerically solving the flow equations defined over a larger semi-infinite domain [0, ∞) using spectral quasilinearization method embedded on overlapping sub-intervals. This method is better than its counterpart on a single domain as it maintains high accuracy and at the same time results in a sparse differentiation matrix that is easily invertible and saves CPU time. The numerical simulations and solution error analysis were performed using MATLAB version 2018a. Convergence analysis demonstrates exponential error decay, with residual errors reducing from the order of 10−2 to approximately 10−12 within four iterations, confirming the accuracy and efficiency of the numerical scheme. Additionally, the impact of the Prandtl number on thermal boundary layer thickness is examined, revealing sharper temperature gradients for higher Pr values. This method can be adapted to solve other fluid flow problems represented as systems of nonlinear ODEs. VL - 13 IS - 4 ER -
Department of Mathematcs, Statistics and Physical Sciences, Taita Taveta University, Voi, Kenya
Department of Mathematcs, Statistics and Physical Sciences, Taita Taveta University, Voi, Kenya
Department of Mathematics and Actuarial Sciences, The Catholic University of Eastern Africa, Nairobi, Kenya
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