In this work, we present the one-dimensional heat 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 paper, 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 heat equation using the principle of Galerkin’s method. The numerical solution is calculated, using the parametrization of the domain and using the numerical integration of Gauss. Solving this partial differential equation leads to solving a system of differential equations. This system will be solved using the classic fourth-order Runge-Kutta method and a CFL condition. Numerical tests have been presented to show the efficiency of this method.
| Published in | Applied and Computational Mathematics (Volume 15, Issue 2) |
| DOI | 10.11648/j.acm.20261934.11 |
| Page(s) | 49-59 |
| 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), 2026. Published by Science Publishing Group |
B-splines, Isogeometric Method, Galerkin Method, Heat Equation, Parametrization, a CFL Condition
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APA Style
Uriel-Longin, A. W., Siba, K., Daugny, T. M. H., Sihintoe, B. M., D, C. B., et al. (2026). A Meshless Method for Solving 1D Heat Equation on a Semicircle. Applied and Computational Mathematics, 15(2), 49-59. https://doi.org/10.11648/j.acm.20261934.11
ACS Style
Uriel-Longin, A. W.; Siba, K.; Daugny, T. M. H.; Sihintoe, B. M.; D, C. B., et al. A Meshless Method for Solving 1D Heat Equation on a Semicircle. Appl. Comput. Math. 2026, 15(2), 49-59. doi: 10.11648/j.acm.20261934.11
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Download@article{10.11648/j.acm.20261934.11,
author = {Aguemon Wiwegnon Uriel-Longin and Kalivogui Siba and Tchiekre Michel Henri Daugny and Badiane Marcel Sihintoe and Coulibaly Bakary D and Bah Thierno Mamadou},
title = {A Meshless Method for Solving 1D Heat Equation on a Semicircle
},
journal = {Applied and Computational Mathematics},
volume = {15},
number = {2},
pages = {49-59},
doi = {10.11648/j.acm.20261934.11},
url = {https://doi.org/10.11648/j.acm.20261934.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20261934.11},
abstract = {In this work, we present the one-dimensional heat 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 paper, 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 heat equation using the principle of Galerkin’s method. The numerical solution is calculated, using the parametrization of the domain and using the numerical integration of Gauss. Solving this partial differential equation leads to solving a system of differential equations. This system will be solved using the classic fourth-order Runge-Kutta method and a CFL condition. Numerical tests have been presented to show the efficiency of this method.
},
year = {2026}
}
TY - JOUR T1 - A Meshless Method for Solving 1D Heat Equation on a Semicircle AU - Aguemon Wiwegnon Uriel-Longin AU - Kalivogui Siba AU - Tchiekre Michel Henri Daugny AU - Badiane Marcel Sihintoe AU - Coulibaly Bakary D AU - Bah Thierno Mamadou Y1 - 2026/03/18 PY - 2026 N1 - https://doi.org/10.11648/j.acm.20261934.11 DO - 10.11648/j.acm.20261934.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 49 EP - 59 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20261934.11 AB - In this work, we present the one-dimensional heat 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 paper, 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 heat equation using the principle of Galerkin’s method. The numerical solution is calculated, using the parametrization of the domain and using the numerical integration of Gauss. Solving this partial differential equation leads to solving a system of differential equations. This system will be solved using the classic fourth-order Runge-Kutta method and a CFL condition. Numerical tests have been presented to show the efficiency of this method. VL - 15 IS - 2 ER -
Mathematics Department, Faculty of Sciences, University of Kindia (UK)
Mathematics Department, Faculty of Sciences, University of Kindia (UK)
Department of Mathematics, Physics and Chemistry, UPR Mathematics, University Peleforo Gon Coulibaly of Korhogo
Mathematics Department, Faculty of Sciences, University of Kindia (UK)
Mathematics Department, Faculty of Sciences, University of Kindia (UK)
Mathematics Department, Faculty of Sciences, University of Kindia (UK)
