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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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.
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...
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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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Views:
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.
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...
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