We present a systematic methodology to develop high order accurate numerical approaches for linear advection problems. These methods are based on evolving parts of the jet of the solution in time,… (More)

Classical random matrix models are formed from dense matrices with Gaussian entries. Their eigenvalues have features that have been observed in combinatorics, statistical mechanics, quantum… (More)

In an online decision problem, an algorithm performs a sequence of trials, each of which involves selecting one element from a fixed set of alternatives (the “strategy set”) whose costs vary over… (More)

Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or… (More)

Pak-Wing Fok,1 Rodolfo R. Rosales,2 and Dionisios Margetis3 1Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125, USA 2Department of Mathematics,… (More)

We present a multirate method that is particularly suited for integrating the systems of Ordinary Differential Equations (ODEs) that arise in step models of surface evolution. The surface of a… (More)

In this paper we present a method to treat interface jump conditions for constant coefficients Poisson problems that allows the use of standard “black box” solvers, without compromising accuracy. The… (More)

Pak-Wing Fok,1,2 Rodolfo R. Rosales,3 and Dionisios Margetis4 1Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125, USA 2Department of… (More)

Fundamental diagrams of vehicular traffic flow are generally multivalued in the congested flow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple… (More)