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

Authors:
Z. Jackiewicz;M. Rahman;B. D. Welfert
Affiliations:
Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA;Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA;Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA
Venue:
Applied Numerical Mathematics
Year:
2006

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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.