In this paper, we present the one-dimensional transport equation solving by the isogeometric method, a meshless method using Galerkin Method. This equation has been solved on a semicircle, a curve on ℝ2. The basis of approximation used for this work, is the B-splines basis. We define univariate B-splines. We look at their properties as well as b-splines curves. We calculate the numerical solution of the transport equation using the principle of Galerkin’s method. The Galerkin method approximates the solution of a differential equation by projecting the original problem onto a finite-dimensional subspace. This approach ensures that the residual defined as the error between the exact and approximate solutions, is orthogonal to this subspace. The numerical solution is calculated, using the parametrization of the domain and using the numerical integration of Gauss. Numerical tests have been presented to show the efficiency of this method.
| Published in | Pure and Applied Mathematics Journal (Volume 14, Issue 4) |
| DOI | 10.11648/j.pamj.20251404.12 |
| Page(s) | 93-101 |
| 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 |
B-splines, Isogeometric Method, Galerkin Method, Transport Equation, Parametrization
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APA Style
Uriel-Longin, A. W., Siba, K., D, C. B. (2025). A Meshless Method for Solving 1D Transport Equation on a Curve of ℝ2. Pure and Applied Mathematics Journal, 14(4), 93-101. https://doi.org/10.11648/j.pamj.20251404.12
ACS Style
Uriel-Longin, A. W.; Siba, K.; D, C. B. A Meshless Method for Solving 1D Transport Equation on a Curve of ℝ2. Pure Appl. Math. J. 2025, 14(4), 93-101. doi: 10.11648/j.pamj.20251404.12
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Download@article{10.11648/j.pamj.20251404.12,
author = {Aguemon Wiwegnon Uriel-Longin and Kalivogui Siba and Coulibaly Bakary D},
title = {A Meshless Method for Solving 1D Transport Equation on a Curve of ℝ2
},
journal = {Pure and Applied Mathematics Journal},
volume = {14},
number = {4},
pages = {93-101},
doi = {10.11648/j.pamj.20251404.12},
url = {https://doi.org/10.11648/j.pamj.20251404.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20251404.12},
abstract = {In this paper, we present the one-dimensional transport equation solving by the isogeometric method, a meshless method using Galerkin Method. This equation has been solved on a semicircle, a curve on ℝ2. The basis of approximation used for this work, is the B-splines basis. We define univariate B-splines. We look at their properties as well as b-splines curves. We calculate the numerical solution of the transport equation using the principle of Galerkin’s method. The Galerkin method approximates the solution of a differential equation by projecting the original problem onto a finite-dimensional subspace. This approach ensures that the residual defined as the error between the exact and approximate solutions, is orthogonal to this subspace. The numerical solution is calculated, using the parametrization of the domain and using the numerical integration of Gauss. Numerical tests have been presented to show the efficiency of this method.
},
year = {2025}
}
TY - JOUR T1 - A Meshless Method for Solving 1D Transport Equation on a Curve of ℝ2 AU - Aguemon Wiwegnon Uriel-Longin AU - Kalivogui Siba AU - Coulibaly Bakary D Y1 - 2025/08/20 PY - 2025 N1 - https://doi.org/10.11648/j.pamj.20251404.12 DO - 10.11648/j.pamj.20251404.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 93 EP - 101 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20251404.12 AB - In this paper, we present the one-dimensional transport equation solving by the isogeometric method, a meshless method using Galerkin Method. This equation has been solved on a semicircle, a curve on ℝ2. The basis of approximation used for this work, is the B-splines basis. We define univariate B-splines. We look at their properties as well as b-splines curves. We calculate the numerical solution of the transport equation using the principle of Galerkin’s method. The Galerkin method approximates the solution of a differential equation by projecting the original problem onto a finite-dimensional subspace. This approach ensures that the residual defined as the error between the exact and approximate solutions, is orthogonal to this subspace. The numerical solution is calculated, using the parametrization of the domain and using the numerical integration of Gauss. Numerical tests have been presented to show the efficiency of this method. VL - 14 IS - 4 ER -
Department of Mathematics, University of Kindia (UK), Kindia, Guinea
Department of Mathematics, University of Kindia (UK), Kindia, Guinea
Department of Mathematics, University of Kindia (UK), Kindia, Guinea
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