A Walsh function method for a non-linear Volterra integral equation
type: Item
instance of: scholarly article
title: A Walsh function method for a non-linear Volterra integral equation
zbMATH Open document ID: 1023.65141
DOI: 10.1016/S0016-0032(02)00052-2
author: B. G. Sloss
author: William F. Blyth
published in: Journal of the Franklin Institute
publication date: 2003-06-10T00:00:00Z
review text: The discontinuous Walsh functions which may be expressed in terms of the Haar functions, and can be obtained from the Rademacher system, form wavelet packets which are applied to a novel method for numerical solution of nonlinear Volterra integral equations. The presentation is clear and detailed: after an extended introduction and information on Walsh functions the solution method is explained carefully with conditions for the convergence of the method and a priori error estimates. The derived method is illustrated by means of two examples with analytical solutions: (i) a linear integral equation where the errors behave as expected, and (ii) a nonlinear integral equation which is solved also using the forward Euler method, besides the method in question; the numerical results are presented in detail (an obvious typo in (55)).
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 1925358
zbMATH Keywords: Walsh functions
zbMATH Keywords: numerical analysis
zbMATH Keywords: Volterra integral equations
zbMATH Keywords: nonlinear
zbMATH Keywords: a priori error estimates
zbMATH Keywords: Haar functions
zbMATH Keywords: Rademacher system
zbMATH Keywords: wavelet packets
zbMATH Keywords: nonlinear Volterra integral equations
zbMATH Keywords: convergence
zbMATH Keywords: forward Euler method
zbMATH Keywords: numerical results
reviewed by: Søren Christiansen
MaRDI profile type: Publication
cites work: A pseudospectral Walsh function method
cites work: Q3028253
cites work: Walsh-fourier series and the concept of a derivative†
cites work: A Walsh series direct method for solving variational problems
cites work: A state-space approach to Walsh series solution of linear systems
cites work: Walsh operational matrices for fractional calculus and their application to distributed systems
cites work: A priori error estimates for Corrington's Walsh function method
cites work: Corrington's Walsh function method applied to a nonlinear integral equation
cites work: Q4214926
cites work: A mathematical introduction to wavelets
cites work: A Remarkable Series of Orthogonal Functions (I)
cites work: On the Walsh Functions
full work available at URL: s0016-0032(02)00052-2
OpenAlex ID: W2065608552
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description: scientific article; zbMATH DE number 1925358