On some iterative numerical methods for a Volterra functional integral equation of the second kind
type: Item
instance of: scholarly article
title: On some iterative numerical methods for a Volterra functional integral equation of the second kind
zbMATH Open document ID: 1382.65471
author: Sanda Micula
published in: Journal of Fixed Point Theory and Applications
publication date: 2017-12-22T00:00:00Z
review text: The paper is concerned with the numerical solution of a nonlinear Volterra integral equation of the form \[ x\left(t\right) = \lambda \int\limits_{-t}^{t} K\left(t,s,x\left(s\right)\right) d s + f\left(t\right), \quad t \in \left[-T,T\right], \] where the kernel \(K\) and the function \(f\) are continuous. The existence and uniqueness of the solution is proved under additional assumptions on the kernel. The author proposes a method that is based on the Picard's successive approximations and trapezoidal rule for computing integrals. The error estimates for the proposed method are derived and numerical experiments are presented to confirm the theoretical results.
reviewed by: Dana Černá
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 6821149
zbMATH Keywords: Picard's successive approximations
zbMATH Keywords: trapezoidal rule
zbMATH Keywords: nonlinear Volterra integral equation
zbMATH Keywords: error estimate
zbMATH Keywords: numerical experiment
MaRDI profile type: Publication
full work available at URL: s11784-016-0336-6
OpenAlex ID: W2534904951
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DOI: 10.1007/S11784-016-0336-6
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description: scientific article; zbMATH DE number 6821149