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Differential equations, Partial - Numerical solutions - Congresses. --- Boundary value problems - Numerical solutions - Congresses. --- Singularities (Mathematics) - Congresses.

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These Proceedings contain a selection of the lectures given at the conference BAIL 2008: Boundary and Interior Layers – Computational and Asymptotic Methods, which was held from 28th July to 1st August 2008 at the University of Limerick, Ireland. The ?rst three BAIL conferences (1980, 1982, 1984) were organised by Professor John Miller in Trinity College Dublin, Ireland. The next seven were held in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth (2002),Toulouse(2004),and Got ¨ tingen(2006).With BAIL 2008the series returned to Ireland. BAIL 2010 is planned for Zaragoza. The BAIL conferences strive to bring together mathematicians and engineers whose research involves layer phenomena,as these two groups often pursue largely independent paths. BAIL 2008, at which both communities were well represented, succeeded in this regard. The lectures given were evenly divided between app- cations and theory, exposing all conference participants to a broad spectrum of research into problems exhibiting solutions with layers. The Proceedings give a good overview of current research into the theory, app- cation and solution (by both numerical and asymptotic methods) of problems that involve boundaryand interior layers. In addition to invited and contributed lectures, the conference included four mini-symposia devoted to stabilized ?nite element methods, asymptotic scaling of wall-bounded ?ows, systems of singularly p- turbed differential equations, and problems with industrial applications (supported by MACSI, the Mathematics Applications Consortium for Science and Industry). These titles exemplify the mix of interests among the participants.

Boundary value problems -- Asymptotic theory. --- Boundary value problems -- Numerical solutions -- Congresses. --- Boundary value problems -- Numerical solutions. --- Boundary value problems. --- Boundary layer --- Boundary value problems --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Mathematics --- Mathematics - General --- Asymptotic theory --- Asymptotic expansions --- Asymptotic developments --- Mathematics. --- Computer mathematics. --- Numerical analysis. --- Mathematical models. --- Applied mathematics. --- Engineering mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Computational Mathematics and Numerical Analysis. --- Numerical Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis --- Computer science --- Mathematical and Computational Engineering. --- Mathematical and Computational Engineering Applications. --- Data processing.