Applied and Computational Mathematics

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: Mar. 21, 2017
    Accepted: Mar. 22, 2017
    Published: Apr. 11, 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
  • 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: Apr. 30, 2017
    Accepted: May 02, 2017
    Published: May 13, 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