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AMCS/STAT Graduate Seminar: Algorithmic Verification of Linearizability for Ordinary Differential Equations

Start Date: April 19, 2018
End Date: April 19, 2018

By Dr. Dmitry Lyakhov (KAUST)
 
For a nonlinear ordinary differential equation solved with respect to the highest order derivative, we devise two heuristic-free algorithms to check if the equation can be mapped to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie algebra. The second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to determine the point transformation and the coefficients of the linearized equation. The implementation of both algorithms is discussed and their application is illustrated using several examples.
 
Biography: Dr. Dmitry A. Lyakhov is currently a postdoctoral researcher in the Computational Sciences Group within KAUST's Visual Computing Center working with Professor Dominik L. Michels. Before, he was a postdoc in the Joint Institute for Nuclear Research in Moscow (with Professor Vladimir P. Gerdt) and a lecturer at the Belarusian State University. He was graduated with his Ph.D. in mathematics and with a M.Sc. in theoretical physics at the Belarusian State University. He is also an alumnus of the National Academy of Sciences of Belarus. His research comprises algebraic algorithms, mathematical modeling, symbolic computation, and theoretical aspects visual computing. He is ACM SIGSAM member and recipient of ISSAC (2017) Distinguished Paper Award.
 

More Information:

For more info contact: Dr. Dmitry Lyakhov: email: dmitry.lyakhov@kaust.edu.sa
 
Date: Thursday 19th Apr 2018
Time:12:00 PM - 01:00 PM
Location: Building 9, Lecture Hall 1 Room 2322
Refreshments: Brown bag Lunch will be provided at 11:45 AM