Spectral collocation methods for Volterra-integro differential equations with noncompact kernels
type: Item
instance of: scholarly article
title: Spectral collocation methods for Volterra-integro differential equations with noncompact kernels
zbMATH Open document ID: 1263.65134
author: Jingtang Ma
author: Ying-Jun Jiang
published in: Journal of Computational and Applied Mathematics
publication date: 2013-02-21T00:00:00Z
review text: The paper is devoted to a study of a numerical method for the linear Volterra integro-differential equation \(y'(t) + a(t) y(t) = \int_0^t s^{\mu-1}t^{-\mu} k(t,s) y(s) ds + g(t)\), \(t \in [0,T]\), subject to the initial condition \(y(0) = y_0\), with sufficiently smooth functions \(a\), \(g\) and \(k\) and \(\mu > 0\). The integral operator in this equation is not compact; this property makes the investigation more difficult. The authors begin by providing sufficient conditions for the existence and uniqueness of solutions and prove regularity properties of these solutions. Then, a spectral collocation method based on Chebyshev polynomials is developed and its convergence is analyzed.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45A05
zbMATH DE Number: 6138051
zbMATH Keywords: noncompact kernels
zbMATH Keywords: spectral collocation methods
zbMATH Keywords: linear Volterra integro-differential equation
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.cam.2012.10.033
OpenAlex ID: W1996037589
DOI: 10.1016/J.CAM.2012.10.033
description: scientific article; zbMATH DE number 6138051