Journal of Integral Equations and Applications

Solving Volterra integral equations of the second kind by sigmoidal functions approximation

Danilo Costarelli and Renato Spigler

Full-text: Open access

Abstract

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.

Article information

Source
J. Integral Equations Applications, Volume 25, Number 2 (2013), 193-222.

Dates
First available in Project Euclid: 4 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1383573822

Digital Object Identifier
doi:10.1216/JIE-2013-25-2-193

Mathematical Reviews number (MathSciNet)
MR3161612

Zentralblatt MATH identifier
1285.65086

Subjects
Primary: 65R20: Integral equations
Secondary: 45D05: Volterra integral equations [See also 34A12] 45G10: Other nonlinear integral equations

Keywords
Collocation methods sigmoidal functions unit step functions linear Volterra integral equations nonlinear Volterra integral equations

Citation

Costarelli, Danilo; Spigler, Renato. Solving Volterra integral equations of the second kind by sigmoidal functions approximation. J. Integral Equations Applications 25 (2013), no. 2, 193--222. doi:10.1216/JIE-2013-25-2-193. https://projecteuclid.org/euclid.jiea/1383573822


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