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Journal of Scientific Computing

Erschienen in:

15.07.2015

Numerical Solutions for Weakly Singular Volterra Integral Equations Using Chebyshev and Legendre Pseudo-Spectral Galerkin Methods

verfasst von: Xianjuan Li, Tao Tang, Chuanju Xu

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2016

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Abstract

In this paper we present and analyze Chebyshev and Legendre pseudo-spectral methods for the second kind Volterra integral equations with weakly singular kernel \((x-s)^{-\mu }, 0<\mu <1\). The proposed methods are based on the Gauss-type quadrature formula for approximating the integral operators involved in the equations. The present work is an extension of the earlier proposed spectral Jacobi–Galerkin method for the second kind Volterra integral equations with regular kernels (Xie et al. in J Sci Comput 53(2):414–434, [21]). A detailed convergence analysis is carried out, and several error estimates in \(L^{\infty } \) and \( L^2_{\omega }\) norms are obtained. Numerical examples are considered to verify the theoretical predictions.

Vorheriger Artikel A Mixed Finite Element Discretisation of Thin Plate Splines Based on Biorthogonal Systems

Nächster Artikel Galerkin Spectral Approximation of Elliptic Optimal Control Problems with -Norm State Constraint

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Titel: Numerical Solutions for Weakly Singular Volterra Integral Equations Using Chebyshev and Legendre Pseudo-Spectral Galerkin Methods
verfasst von: Xianjuan Li
Tao Tang
Chuanju Xu
Publikationsdatum: 15.07.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0069-5

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