Daniel Michelson
My research involves differential
equations that are used to describe a continuous media like the atmosphere,
ocean waves or flames. My aim is to narrow the gap between the applied mathematicians
that derive appropriate models but solve them only approximately, due to shortcomings
of the means of computations, and the theoretical mathematicians that can provide
rigorous results but for equations that are far away from the physical reality.
Narrowing the gap is done with computer assisted proofs. Here the computer estimates
its own round-off errors and thus is able to provide rigorous results. Using
this technique I was able to analyze the stability of Bunsen flames and design
accurate schemes for computing shock waves that arise in aerodynamics. Recently
I became involved in the study of predictability of lunar motion and verification
of different events in the remote past. In particular, explanation is given
for the strange orientation of the walls of the Temple Mount in Jerusalem.
Recent Publications
- Stability of discrete shocks for difference approximations to systems of conservation laws. SIAM Journal of Numerical Analysis 40: 3 (2002) 820-871.
- Radial asymptotically periodic solutions of the Kuramoto-Sivashinsky equation. Physica D 237: 3 (2008) 351-358.