Open Access
SUMMER 2013 Solving Volterra integral equations of the second kind by sigmoidal functions approximation
Danilo Costarelli, Renato Spigler
J. Integral Equations Applications 25(2): 193-222 (SUMMER 2013). DOI: 10.1216/JIE-2013-25-2-193


In this paper, a numerical collocation method is developed for solving linear and nonlinear Volterra integral equations of the second kind. The method is based on the approximation of the (exact) solution by a superposition of sigmoidal functions and allows one to solve a large class of integral equations having either continuous or $L^p$ solutions. Special computational advantages are obtained using unit step functions, and analytical approximations of the solution are also at hand. The numerical errors are discussed, and a priori as well as a posteriori estimates are derived for them. Numerical examples are given for the purpose of illustration.


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Danilo Costarelli. Renato Spigler. "Solving Volterra integral equations of the second kind by sigmoidal functions approximation." J. Integral Equations Applications 25 (2) 193 - 222, SUMMER 2013.


Published: SUMMER 2013
First available in Project Euclid: 4 November 2013

zbMATH: 1285.65086
MathSciNet: MR3161612
Digital Object Identifier: 10.1216/JIE-2013-25-2-193

Primary: 65R20
Secondary: 45D05 , 45G10

Keywords: collocation methods , linear Volterra integral equations , nonlinear Volterra integral equations , sigmoidal functions , unit step functions

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

Vol.25 • No. 2 • SUMMER 2013
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