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
Approximate solution to Fredholm integral equations using linear regression and applications to heat and mass transfer. / Ioannou, Yiannos; Fyrillas, Marios M.; Doumanidis, Charalabos.
In: Engineering Analysis with Boundary Elements, Vol. 36, No. 8, 08.2012, p. 1278-1283.Research output: Contribution to journal › Article
}
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 -