Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind
type: Item
instance of: scholarly article
title: Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind
zbMATH Open document ID: 1260.65111
author: Xianjuan Li
author: Tao Tang
published in: Frontiers of Mathematics in China
publication date: 2012-11-15T00:00:00Z
review text: The authors extend the known method of collocations to approximate solving a Volterra integral equation with the singular kernel \[ y(t) = g(t)+ \int_{0}^{t} (t-s)^{\mu} K(t,s)y(s)ds \] for the case \(\mu =1/2\). The convergence of this method is proved using the quadrature formulas defined by Jacobi polynomials, but for numerical experiments only the Lagrangian polynomials are used.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 6107738
zbMATH Keywords: Jacobi spectral collocation method
zbMATH Keywords: Abel-Volterra singular integral equation
zbMATH Keywords: convergence
zbMATH Keywords: quadrature formula method
zbMATH Keywords: numerical experiments
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
full work available at URL: s11464-012-0170-0
OpenAlex ID: W2055212013
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DOI: 10.1007/S11464-012-0170-0
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description: scientific article; zbMATH DE number 6107738