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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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
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.
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.
Copyright © 2017 Authors retain the copyright of this article.
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