|Erik Van Vleck||Time Dependent Stability of Numerical Methods|
|Classical stability theory for numerical time stepping techniques for the solution of initial value differential equations, though largely motivated by time dependent solutions, is dominated by techniques for time independent solutions. Building on work of Luca and his collaborators on computational time dependent stability theory, we present some recent results and perspectives on the development of time dependent stability theory for numerical methods aimed at improving the accuracy and efficiency of numerical methods.|
|Cinzia Elia||Periodic orbits of discontinuous DEs: numerical remarks|
We consider a planar linear discontinuous system with a globally asymptotically stable periodic orbit and we study the qualitative behavior of the numerical approximation obtained with forward Euler with and without event location. Differences and similarities with the theory for smooth systems will be highlighted and justified both numerically and theoretically.
|Yingfei Yi||Reducibility of Quasi-Periodic Linear KdV Equation|
We consider a family of perturbative, one-dimensional, quasi-periodically forced, linear KdV equations under the periodic boundary condition. Under the real analyticity and symmetry assumptions of the coefficients, we show that there exists a Cantor set in the frequency domain on which the corresponding equations are smoothly reducible to constant-coefficients ones This problem is closely related to the existence and linear stability of quasi-periodic solutions in a nonlinear KdV equation.
|Michael Li||Limit Threshold Results for Stochastic Epidemic Models|
By analyzing master equations, we show that a Markov chain model for infectious diseases can possess sharp threshold results as in the deterministic epidemic models, as the population size tends to infinity.
|Wuchen Li||Entropy dissipation semi-discretization schemes for Fokker-Planck equations|
|Fokker-Planck equations are important for modeling and applications. In this talk, we consider a numerical method towards them based on optimal transport theory. Many details and properties of numerics will be introduced. This is a joint work with Shui-Nee Chow, Luca Dieci and Haomin Zhou.|
|JD Walsh||An auction algorithm for real-valued optimal transport|
|In commerce, auctions are a time-tested method of obtaining optimal object prices from a group of competing bidders. In the 1970s, Dimitri Bertsekas developed an auction-based algorithm, as an alternative to the Hungarian method for the assignment problem. He and David Castañón later published an auction algorithm for integer-valued optimal transport that solves by converting transport problems into assignment problems. We propose a more general auction algorithm that works directly on real-valued transport problems and describe its connection to the algorithm of Bertsekas and Castañón.|