### 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) |
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Pages (from-to) | 423-432 |

Number of pages | 10 |

Journal | Applied Numerical Mathematics |

Volume | 56 |

Issue number | 3-4 SPEC. ISS. |

DOIs | |

State | Published - Mar 2006 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation

### Cite this

*Applied Numerical Mathematics*,

*56*(3-4 SPEC. ISS.), 423-432. https://doi.org/10.1016/j.apnum.2005.04.020

**Numerical solution of a Fredholm integro-differential equation modelling neural networks.** / Jackiewicz, Zdzislaw; Rahman, M.; Welfert, Bruno.

Research output: Contribution to journal › Article

*Applied Numerical Mathematics*, vol. 56, no. 3-4 SPEC. ISS., pp. 423-432. https://doi.org/10.1016/j.apnum.2005.04.020

}

TY - JOUR

T1 - Numerical solution of a Fredholm integro-differential equation modelling neural networks

AU - Jackiewicz, Zdzislaw

AU - Rahman, M.

AU - Welfert, Bruno

PY - 2006/3

Y1 - 2006/3

N2 - 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.

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.

KW - Euler-Hermite and Euler-Laguerre method

KW - Fredholm integro-differential equation

KW - Neural networks

UR - http://www.scopus.com/inward/record.url?scp=33644624159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644624159&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2005.04.020

DO - 10.1016/j.apnum.2005.04.020

M3 - Article

AN - SCOPUS:33644624159

VL - 56

SP - 423

EP - 432

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

IS - 3-4 SPEC. ISS.

ER -