Numerical solution of a Fredholm integro-differential equation modelling neural networks

Zdzislaw Jackiewicz; M. Rahman; Bruno Welfert

doi:10.1016/j.apnum.2005.04.020

Numerical solution of a Fredholm integro-differential equation modelling neural networks

Zdzislaw Jackiewicz, M. Rahman, Bruno Welfert

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

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

20 Scopus citations

Abstract

We compare piecewise linear and polynomial collocation approaches for the numerical solution of a Fredholm integro-differential equations modelling neural networks. Both approaches combine the use of Gaussian quadrature rules on an infinite interval of integration with interpolation to a uniformly distributed grid on a bounded interval. These methods are illustrated by numerical experiments on neural networks equations.

Original language	English (US)
Pages (from-to)	423-432
Number of pages	10
Journal	Applied Numerical Mathematics
Volume	56
Issue number	3-4 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.apnum.2005.04.020
State	Published - Mar 2006

Keywords

Euler-Hermite and Euler-Laguerre method
Fredholm integro-differential equation
Neural networks

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/j.apnum.2005.04.020

Cite this

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title = "Numerical solution of a Fredholm integro-differential equation modelling neural networks",

abstract = "We compare piecewise linear and polynomial collocation approaches for the numerical solution of a Fredholm integro-differential equations modelling neural networks. Both approaches combine the use of Gaussian quadrature rules on an infinite interval of integration with interpolation to a uniformly distributed grid on a bounded interval. These methods are illustrated by numerical experiments on neural networks equations.",

keywords = "Euler-Hermite and Euler-Laguerre method, Fredholm integro-differential equation, Neural networks",

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

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AU - Rahman, M.

AU - Welfert, Bruno

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AB - We compare piecewise linear and polynomial collocation approaches for the numerical solution of a Fredholm integro-differential equations modelling neural networks. Both approaches combine the use of Gaussian quadrature rules on an infinite interval of integration with interpolation to a uniformly distributed grid on a bounded interval. These methods are illustrated by numerical experiments on neural networks equations.

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KW - Fredholm integro-differential equation

KW - Neural networks

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JO - Applied Numerical Mathematics

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ER -

Numerical solution of a Fredholm integro-differential equation modelling neural networks

Abstract

Keywords

ASJC Scopus subject areas

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