Rochester Institute of Technology

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Asymptotic Approximants
  • Speaker: Dr Nate Barlow
  • Start Time: 
  • End Time: 
  • Location: CCRG Lounge
  • Type: Lunch Talk

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There are several problems of mathematical physics in which the only available analytic solution is a divergent and/or truncated series expansion. Examples include the Post-Newtonian expansion of general relativity, the thermodynamic virial equation of state, and as-of-yet unsolved integrals and differential equations of fluid dynamics (e.g. Blasius boundary layer ODE) and astrophysics (black hole light bending).  Over the past decade, a new approach has evolved (which we call Asymptotic Approximants for reasons to be explained) to overcome the convergence barrier in such problems.   Simply put, an asymptotic approximant is a closed-form analytic expression whose expansion in one region is exact up to a specified order and whose limit in another region is also exact.  The remarkable feature of asymptotic approximants is their ability to attain uniform accuracy not only at the two regions enforced, but also at all points in-between.   In this talk, I will demonstrate how to construct an asymptotic approximant via recursion (no matrix inversion required).  I will also present a history of the success of asymptotic approximants in providing uniformly accurate analytic solutions to problems of thermodynamics, fluid dynamics, and astrophysics.