We study regularity of solutions of weakly singular Volterra integral equations of the first kind. We then study the numerical analysis of discontinuous piecewise polynomial collocation methods for solving such systems. The main purpose of this paper is the derivation of global convergent and super-convergent properties of introduced methods on the graded meshes. We apply relevant methods to a system of fractional differential equations and analyze them. The numerical experiments confirm the theoretical results.
| Published in |
Applied and Computational Mathematics (Volume 7, Issue 1-1)
This article belongs to the Special Issue Singular Integral Equations and Fractional Differential Equations |
| DOI | 10.11648/j.acm.s.2018070101.11 |
| Page(s) | 1-11 |
| 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), 2024. Published by Science Publishing Group |
Discontinuous Piecewise Polynomial Spaces, Collocation Methods, Graded Meshes, Weakly Singular Volterra Integral Equations
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APA Style
Gholamreza Karamali, Babak Shiri, Mahnaz Kashfi. (2017). Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind. Applied and Computational Mathematics, 7(1-1), 1-11. https://doi.org/10.11648/j.acm.s.2018070101.11
ACS Style
Gholamreza Karamali; Babak Shiri; Mahnaz Kashfi. Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind. Appl. Comput. Math. 2017, 7(1-1), 1-11. doi: 10.11648/j.acm.s.2018070101.11
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Download@article{10.11648/j.acm.s.2018070101.11,
author = {Gholamreza Karamali and Babak Shiri and Mahnaz Kashfi},
title = {Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind},
journal = {Applied and Computational Mathematics},
volume = {7},
number = {1-1},
pages = {1-11},
doi = {10.11648/j.acm.s.2018070101.11},
url = {https://doi.org/10.11648/j.acm.s.2018070101.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2018070101.11},
abstract = {We study regularity of solutions of weakly singular Volterra integral equations of the first kind. We then study the numerical analysis of discontinuous piecewise polynomial collocation methods for solving such systems. The main purpose of this paper is the derivation of global convergent and super-convergent properties of introduced methods on the graded meshes. We apply relevant methods to a system of fractional differential equations and analyze them. The numerical experiments confirm the theoretical results.},
year = {2017}
}
TY - JOUR T1 - Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind AU - Gholamreza Karamali AU - Babak Shiri AU - Mahnaz Kashfi Y1 - 2017/04/11 PY - 2017 N1 - https://doi.org/10.11648/j.acm.s.2018070101.11 DO - 10.11648/j.acm.s.2018070101.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 1 EP - 11 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.s.2018070101.11 AB - We study regularity of solutions of weakly singular Volterra integral equations of the first kind. We then study the numerical analysis of discontinuous piecewise polynomial collocation methods for solving such systems. The main purpose of this paper is the derivation of global convergent and super-convergent properties of introduced methods on the graded meshes. We apply relevant methods to a system of fractional differential equations and analyze them. The numerical experiments confirm the theoretical results. VL - 7 IS - 1-1 ER -
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