A Convergence Analysis of Discontinuous Collocation Method for IAEs of Index 1 Using the Concept “Strongly Equivalent”
Applied and Computational Mathematics
Volume 7, Issue 1-1, January 2018, Pages: 12-17
Received: Apr. 30, 2017; Accepted: May 2, 2017; Published: May 13, 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
Elham Sefidgar, Atatürk University Faculty of Science, Department of Mathematics, Erzurum, Turkey
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Abstract
We introduce the concept “strongly equivalent” for integral algebraic equations (IAEs). This definition and its corresponding theorems construct powerful tools for the classifying and analyzing of IAEs (especially numerical analysis). The related theorems with short proofs provide powerful techniques for the complete convergence analysis of discretised collocation methods on discontinuous piecewise polynomial spaces.
Keywords
Volterra Integral Equation, Volterra Equation, Integral equation, Discontinuous Piecewise Polynomial Spaces, Collocation Methods
To cite this article
Gholamreza Karamali, Babak Shiri, Elham Sefidgar, A Convergence Analysis of Discontinuous Collocation Method for IAEs of Index 1 Using the Concept “Strongly Equivalent”, Applied and Computational Mathematics. Special Issue:Singular Integral Equations and Fractional Differential Equations. Vol. 7, No. 1-1, 2018, pp. 12-17. doi: 10.11648/j.acm.s.2018070101.12
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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