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SUMMARY:Numerical Solution of Sturm-Liouville Problems via Fer Streamers -
  Alberto Gil Ramos (CCA/DAMTP)
DTSTART:20140528T150000Z
DTEND:20140528T160000Z
UID:TALK52359@talks.cam.ac.uk
CONTACT:Vittoria Silvestri
DESCRIPTION:We address the numerical challenge of solving Sturm--Liouville
  problems in Liouville's normal form\, with regular boundary conditions an
 d a continuous and piecewise analytic potential. The novelty of our approa
 ch\, which is based on a non-standard truncation of Fer expansions\, which
  we call `Fer streamers'\, lies in the construction of a new numerical met
 hod\, which\, \\emph{i}) does not impose any restriction on the step size 
 for eigenvalues which are greater or equal than the minimum of the potenti
 al\, \\emph{ii}) requires only a mild restriction on the step size for the
  remaining finite number of eigenvalues\, \\emph{iii}) can attain any conv
 ergence rate\, which grows exponentially with the number of terms\, and is
  uniform for every eigenvalue\, and\, \\emph{iv}) lends itself to a clear 
 understanding of the manner in which the potential affects the local and g
 lobal errors. We provide our numerical method with its analytical underpin
 ning\, but emphasize that it is at an early stage of development and that 
 much remains to be done. In particular\, we comment on our investigation o
 f efficient discretization schemes for the integrals which arise in Fer st
 reamers.
LOCATION:MR14\, Centre for Mathematical Sciences
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