Archive:: Applied and Computational Mathematics:: Science Publishing Group

Volume 7, Issue 1, January 2018

Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind

Gholamreza Karamali, Babak Shiri, Mahnaz Kashfi

Issue: Volume 7, Issue 1-1, January 2018

Pages: 1-11

Received: 21 March 2017

Accepted: 22 March 2017

Published: 11 April 2017

DOI: 10.11648/j.acm.s.2018070101.11

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This article belongs to the Special Issue Singular Integral Equations and Fractional Differential Equations

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... Show More

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A Convergence Analysis of Discontinuous Collocation Method for IAEs of Index 1 Using the Concept “Strongly Equivalent”

Gholamreza Karamali, Babak Shiri, Elham Sefidgar

Issue: Volume 7, Issue 1-1, January 2018

Pages: 12-17

Received: 30 April 2017

Accepted: 2 May 2017

Published: 13 May 2017

DOI: 10.11648/j.acm.s.2018070101.12

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This article belongs to the Special Issue Singular Integral Equations and Fractional Differential Equations

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 discret... Show More

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