Numerical solution of a Fredholm integro-differential equation modelling over(θ, ̇)-neural networks

Zdzislaw Jackiewicz; M. Rahman; Bruno Welfert

doi:10.1016/j.amc.2007.05.031

Numerical solution of a Fredholm integro-differential equation modelling over(θ, ̇)-neural networks

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We propose several approaches to the numerical solution of a new Fredholm integro-differential equations modelling neural networks. A solution strategy based on expansions onto standard cardinal basis functions and collocation is presented. Comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are used to motivate alternate strategies.

Original language	English (US)
Pages (from-to)	523-536
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	195
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2007.05.031
State	Published - Feb 1 2008

Keywords

Collocation
Fredholm integro-differential equation
Gaussian quadrature
Neural networks
Piecewise linear approximation
Polynomial approximation
Pseudospectral methods
Rational approximation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2007.05.031

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title = "Numerical solution of a Fredholm integro-differential equation modelling over(θ,{\. })-neural networks",

abstract = "We propose several approaches to the numerical solution of a new Fredholm integro-differential equations modelling neural networks. A solution strategy based on expansions onto standard cardinal basis functions and collocation is presented. Comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are used to motivate alternate strategies.",

keywords = "Collocation, Fredholm integro-differential equation, Gaussian quadrature, Neural networks, Piecewise linear approximation, Polynomial approximation, Pseudospectral methods, Rational approximation",

author = "Zdzislaw Jackiewicz and M. Rahman and Bruno Welfert",

note = "Funding Information: This work was partially supported by NSF Grant DMS-0510813. ",

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AU - Jackiewicz, Zdzislaw

AU - Rahman, M.

AU - Welfert, Bruno

N1 - Funding Information: This work was partially supported by NSF Grant DMS-0510813.

PY - 2008/2/1

Y1 - 2008/2/1

N2 - We propose several approaches to the numerical solution of a new Fredholm integro-differential equations modelling neural networks. A solution strategy based on expansions onto standard cardinal basis functions and collocation is presented. Comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are used to motivate alternate strategies.

AB - We propose several approaches to the numerical solution of a new Fredholm integro-differential equations modelling neural networks. A solution strategy based on expansions onto standard cardinal basis functions and collocation is presented. Comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are used to motivate alternate strategies.

KW - Collocation

KW - Fredholm integro-differential equation

KW - Gaussian quadrature

KW - Neural networks

KW - Piecewise linear approximation

KW - Polynomial approximation

KW - Pseudospectral methods

KW - Rational approximation

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UR - https://www.scopus.com/pages/publications/37349002670#tab=citedBy

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M3 - Article

AN - SCOPUS:37349002670

SN - 0096-3003

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EP - 536

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Numerical solution of a Fredholm integro-differential equation modelling over(θ, ̇)-neural networks

Abstract

Keywords

ASJC Scopus subject areas

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