TWO APPLICATIONS OF SINGULAR PERTURBATION METHODS
by Associate Professor John Shepherd
Abstract: In this talk, we consider two quite different examples of applying singular perturbation techniques to problems that arise in a physical context.
Slowly varying Population Models
Many single-species differential equation population models feature a 'carrying capacity' -the limiting population supportable by the environment. For constant carrying capacities, an exact solution may often be found, representing the evolving population in time. However, for time-varying carrying capacities, exact solution is rarely possible, and numerical techniques must be used. In this talk, we demonstrate that when the carrying capacity varies slowly with time, a multiple time scale analysis leads to approximate closed form solutions that, apart from being explicit, are at least as accurate as numerically generated ones, and which are valid for a range of parameter values.
We also demonstrate how this analysis can be extended to population models involving a range of slowly varying parameters.
Interior Layers in the Film Blowing Process
Film blowing is a widely used industrial process employed to manufacture thin sheets of polymer used in a wide range of commercial and industrial applications - for example, plastic bags. Realistic mathematical models of this process involve highly nonlinear problems, reflecting the complex physical processes occurring during manufacture.
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