Asymptotic analysis

D. Dominici (Technische Universität Berlin, Germany - SUNY New Paltz, USA) and R. B. Paris (University of Abertay Dundee)

Many of the problems facing mathematicians and scientists involve such difficulties as non-linear governing equations and complex boundary conditions that preclude their exact solution. Consequently, solutions are approximated using numerical techniques, analytic techniques or combinations of both. Foremost among the analytic techniques are the systematic methods of perturbations (asymptotic expansions) in terms of a small or large parameter or coordinate.

The advantage of allowing parameters to become small or large is that in surprisingly many cases, even when there do exist explicit expressions for the functions we are interested in, this procedure does yield simple asymptotic approximations, when the influence of less important factors falls off.

In recent years, asymptotic methods have been used extensively in several fields of pure and applied mathematics including algebra, geometry, analysis, differential and difference equations, probability theory, number theory, special functions and combinatorics.

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