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A numerical method for the solution of second order differential equations in the high-frequency regime

PDE and Applied Math Seminar

Speaker: Jim Bremer, UC Davis
Related Webpage: https://www.math.ucdavis.edu/~bremer/
Location: 2112 MSB
Start time: Fri, May 5 2017, 4:10PM

Classical results on the existence of nonoscillatory phase functions for second order differential equations make clear that there is a class of such equations which can be solved in time independent of the frequency of oscillation of their solutions. Surprisingly, there has been little work on characterizing this class of ODEs or on developing practical numerical algorithms which exploit this observation.

We will discuss a theorem which gives conditions under which nonoscillatory phase functions exist and describe a highly effective algorithm for solving the variable coefficient Helmholtz equation in one spatial dimension. Our algorithm runs in time independent of the frequency of oscillation of solutions.

Not a usual room.