### Abstract

In this work we develop improved asymptotic solutions to one-dimensional Fredholm integral equations of the first kind using linear regression. For the cases under consideration the unknown function is the flux distribution along a strip, and the integral equation depends on a parameter or a number of parameters, i.e. the Péclet number, the Biot number, the dimensionless length scales etc. It is assumed that asymptotic solutions, with respect to the parameters, are available. We show that the asymptotic solutions can be improved and extended by relaxing the coefficients associated with them and applying regression analysis to yield best-fit coefficients. The asymptotic solutions may even be combined to obtain a matched asymptotic expansion. Explicit expressions for the coefficients, which can depend on a number of parameters, are obtained using regression analysis, i.e. by creating a variational principle for the Fredholm Integral Equation and employing the least squares method. The resulting expression, although it provides an approximate solution to the flux distribution, it is explicit and estimates accurately the overall transport rate.

Original language | English |
---|---|

Pages (from-to) | 1278-1283 |

Number of pages | 6 |

Journal | Engineering Analysis with Boundary Elements |

Volume | 36 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2012 |

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### Keywords

- Heat/mass transfer
- Integral equations
- Matched asymptotic expansions
- Regression analysis

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Computational Mathematics
- Engineering(all)

### Cite this

*Engineering Analysis with Boundary Elements*,

*36*(8), 1278-1283. https://doi.org/10.1016/j.enganabound.2012.02.006

**Approximate solution to Fredholm integral equations using linear regression and applications to heat and mass transfer.** / Ioannou, Yiannos; Fyrillas, Marios M.; Doumanidis, Charalabos.

Research output: Contribution to journal › Article

*Engineering Analysis with Boundary Elements*, vol. 36, no. 8, pp. 1278-1283. https://doi.org/10.1016/j.enganabound.2012.02.006

}

TY - JOUR

T1 - Approximate solution to Fredholm integral equations using linear regression and applications to heat and mass transfer

AU - Ioannou, Yiannos

AU - Fyrillas, Marios M.

AU - Doumanidis, Charalabos

PY - 2012/8

Y1 - 2012/8

N2 - In this work we develop improved asymptotic solutions to one-dimensional Fredholm integral equations of the first kind using linear regression. For the cases under consideration the unknown function is the flux distribution along a strip, and the integral equation depends on a parameter or a number of parameters, i.e. the Péclet number, the Biot number, the dimensionless length scales etc. It is assumed that asymptotic solutions, with respect to the parameters, are available. We show that the asymptotic solutions can be improved and extended by relaxing the coefficients associated with them and applying regression analysis to yield best-fit coefficients. The asymptotic solutions may even be combined to obtain a matched asymptotic expansion. Explicit expressions for the coefficients, which can depend on a number of parameters, are obtained using regression analysis, i.e. by creating a variational principle for the Fredholm Integral Equation and employing the least squares method. The resulting expression, although it provides an approximate solution to the flux distribution, it is explicit and estimates accurately the overall transport rate.

AB - In this work we develop improved asymptotic solutions to one-dimensional Fredholm integral equations of the first kind using linear regression. For the cases under consideration the unknown function is the flux distribution along a strip, and the integral equation depends on a parameter or a number of parameters, i.e. the Péclet number, the Biot number, the dimensionless length scales etc. It is assumed that asymptotic solutions, with respect to the parameters, are available. We show that the asymptotic solutions can be improved and extended by relaxing the coefficients associated with them and applying regression analysis to yield best-fit coefficients. The asymptotic solutions may even be combined to obtain a matched asymptotic expansion. Explicit expressions for the coefficients, which can depend on a number of parameters, are obtained using regression analysis, i.e. by creating a variational principle for the Fredholm Integral Equation and employing the least squares method. The resulting expression, although it provides an approximate solution to the flux distribution, it is explicit and estimates accurately the overall transport rate.

KW - Heat/mass transfer

KW - Integral equations

KW - Matched asymptotic expansions

KW - Regression analysis

UR - http://www.scopus.com/inward/record.url?scp=84858982014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858982014&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2012.02.006

DO - 10.1016/j.enganabound.2012.02.006

M3 - Article

AN - SCOPUS:84858982014

VL - 36

SP - 1278

EP - 1283

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

IS - 8

ER -