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 | |
| 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
Numerical solution of a Fredholm integro-differential equation modelling neural networks. / Jackiewicz, Zdzislaw; Rahman, M.; Welfert, Bruno.
In: Applied Numerical Mathematics, Vol. 56, No. 3-4 SPEC. ISS., 03.2006, p. 423-432.Research output: Contribution to journal › Article
}
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 -