Quadratic spline collocation for Volterra integral equations
type: Item
instance of: scholarly article
title: Quadratic spline collocation for Volterra integral equations
zbMATH Open document ID: 1074.65151
DOI: 10.4171/ZAA/1227
author: Darja Saveljeva
author: Peeter Oja
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2005-04-11T00:00:00Z
review text: In the traditional one-step collocation method in the space of \(C^1\)-quadratic splines for second-kind Volterra integral equations, the authors replace one of the required initial conditions by a ``not-a-knot'' boundary condition at the right endpoint of the interval of integration. This nonlocal method yields uniform boundedness of the collocation projection for all collocation parameters \(c\in(0, 1)\). For \(c= 1\) the projection norms exhibit linear growth, and hence for any choice of c appropriate general convergence theorems can be used to establish the convergence based on two-sided error estimates. Numerical illustrations for linear problems with constant (positive or negative) kernels confirm the foregoing analysis.
reviewed by: H. Brunner
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 2155013
zbMATH Keywords: quadratic spline collocation method
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
cites work: The Numerical Solution of Integral Equations of the Second Kind
cites work: Q4151113
cites work: Q5593612
cites work: Runge-Kutta Theory for Volterra Integral Equations of the Second Kind
cites work: Q3750978
cites work: The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
full work available at URL: https://doi.org/10.4171/zaa/1227
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description: scientific article; zbMATH DE number 2155013