Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind
Applied and Computational Mathematics
Volume 7, Issue 1-1, January 2018, Pages: 1-11
Received: Mar. 21, 2017; Accepted: Mar. 22, 2017; Published: Apr. 11, 2017
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Authors
Gholamreza Karamali, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran
Babak Shiri, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran; Department of Applied Mathematics, University of Tabriz, Bahman Boulevard, Tabriz, Iran
Mahnaz Kashfi, Department of Applied Mathematics, University of Tabriz, Bahman Boulevard, Tabriz, Iran
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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.
Keywords
Discontinuous Piecewise Polynomial Spaces, Collocation Methods, Graded Meshes, Weakly Singular Volterra Integral Equations
To cite this article
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, Applied and Computational Mathematics. Special Issue:Singular Integral Equations and Fractional Differential Equations. Vol. 7, No. 1-1, 2018, pp. 1-11. doi: 10.11648/j.acm.s.2018070101.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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