Error analysis of the ultraspherical spectral-collocation method for high-index IAEs

The subject of integral-algebraic equations (IAEs) with index > 2 is new in the literature and there are a few available results which investigate these systems. We will deal here with a particular class of IAEs of index-3 and analyse ultraspherical polynomials collocation method as well as conve...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 94; no. 4; pp. 650 - 662
Main Author Pishbin, S.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.04.2017
Taylor & Francis Ltd
Subjects
Algebra
Approximation
Collocation methods
convergence analysis
Error analysis
index-3
Integral-algebraic equations
Interpolation
Mathematical analysis
Mathematical models
numerical treatment
orthogonal polynomial collocation methods
Polynomials
Spectra
Online AccessGet full text
ISSN0020-7160
1029-0265
DOI10.1080/00207160.2015.1121247

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Summary:The subject of integral-algebraic equations (IAEs) with index > 2 is new in the literature and there are a few available results which investigate these systems. We will deal here with a particular class of IAEs of index-3 and analyse ultraspherical polynomials collocation method as well as convergence analysis for the numerical solution of these systems. Our error analysis of collocation method is based on polynomial approximation theory and results related to the interpolation error in Sobolev space. Numerical examples illustrate the theoretical results.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2015.1121247