Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
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TL;DR: In this article, the authors developed improved asymptotic solutions to one-dimensional Fredholm integral equations of the first kind using linear regression, which can be extended by relaxing the coefficients associated with them and applying regression analysis to yield best-fit coefficients.
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 Peclet 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.
18 citations
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TL;DR: In this article, a closure procedure for the hierarchy of moment equations related to linear systems of ordinary differential equations with a random parametric excitation is introduced, and a generalization of Pringsheim's theorem for continued fractions is used in a proof of the procedure convergence.
18 citations
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TL;DR: In this paper, the authors considered the case of one space dimension with U(X) independent and with the extra term q(x) u included on the left side of (1.1).
18 citations
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18 citations
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18 citations