Natalie E Sheils

Doctoral Candidate in Applied Mathematics
NSF Graduate Research Fellow
University of Washington

Name Natalie E Sheils
Email nsheils (at) uw (dot) edu
Address University of Washington
Department of Applied Mathematics
Lewis Hall, Box 353921
Seattle, WA 98195-3921
Office Lewis Hall 306
Google Scholar Profile Unified Transform Method Portal arXiv
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Natalie E Sheils

I am a Ph.D candidate in Applied Mathematics at the University of Washington. I plan to graduate in June 2015 and have accepted a position as a Visiting Assistant Professor in the School of Mathematics at the University of Minnesota. I am working with Bernard Deconinck on analytic solutions of interface problems using the Unified Transform (Fokas) Method. My research statement is available here.

Prior to studying at UW I earned my undergraduate degree in Mathematics with a specialization in Applied Mathematics at Seattle University. I worked with John Carter on the stability of two-dimensional soltion solutions to the nonlinear Schrödinger equation.


  • Well posedness of linear third order equations with interfaces . In preparation (B. Deconinck, N.E.S. and D.A. Smith)
  • The time-dependent Schrödinger equation with piecewise constant potentials . In preparation (N.E.S. and B. Deconinck)
  • Heat equation on a network using the unified transform method . Submitted for publication (N.E.S and D.A. Smith.).pdf
  • Interface problems for dispersive equations . Stud. Appl. Math., 134 (3): 253-275, 2015 (N.E.S and B. Deconinck ).pdf
  • Heat Conduction on the ring: Interface problems with periodic boundary conditions . Appl. Math. Lett., 37(0): 107-111, 2014 (N.E.S and B. Deconinck ).pdf
  • Non-steady state heat conduciton in composite walls . Proc. Roy. Soc. A, 470 (2165): 22pp., 2014 (B. Deconinck, B. Pelloni, and N.E.S).pdf
  • On the spectral stability of solitary wave solutions of the vector Nonlinear Schrödinger equation. J. Phys. A, 46(41):415202, 22pp., 2013 (B. Deconinck, N.E.S., N. V. Nguyen, and R. Tian) .pdf
  • Global existence for a coupled system of Schrödinger equations with power-type nonlinearites. J. Math. Phys. 54(1): 011503, 19pp., 2013 (N. V. Nguyen, R. Tian, B. Deconinck, and N.E.S) .pdf
  • Entrainment ranges of forced phase oscillators. J. Math. Bio. 62: 5890603, 2011 (J. Previte, N.E.S., K. Hoffman, T. Kiemel, E. Tytell)