Numerical solution of a Fredholm integro-differential equation modelling neural networks. (English) Zbl 1089.65136

Jackiewicz, Z.; Rahman, M. Mahbubur; Welfert, B. D.

Appl. Numer. Math. 56, No. 3-4, 423-432 (2006).

Summary: 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.

MSC:

65R20	Numerical methods for integral equations
45J05	Integro-ordinary differential equations
45G10	Other nonlinear integral equations

Keywords:

Fredholm integro-differential equation; Euler-Hermite method; Euler-Laguerre method; Neural networks; Gaussian quadrature rules; numerical experiments

Software:

mctoolbox

References:

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