Fractional Partial Differential Equations(FPDEs)are emerging as a new powerful tool for modeling many difficult complex systems,i.e.,systems with overlapping microscopic and macroscopic scales or syst
A novel 2nd-order algorithm for Riesz derivatives is established through constructing a new generating function and applying the shift technique.Applying this algorithm to Riesz type partial different
We discuss high-order methods inspired by the multi-step Adams methods for systems of fractional differential equations.The schemes are based on an expansion in a weighted space.We discuss the local t
Isotropic and nematic are two important phases for liquid crystals materials.In this talk,we will discuss the isotropic-nematic problem in the framework of Landau-de Gennes theory.Specifically,we will
We consider multi-component two-phase systems modeled by a diffusive interface model equipped with van der Waals equation of state(EOS).We propose an efficient numerical solution of the modeling syste
Cahn-Hilliard-Navier-Stokes system is one of the well established diffuse interface models for two phase flows.We present a second order in time accurate,unconditionally stable,and uniquely solvable n
When constructing absorbing boundary conditions for discretized hyperbolic PDEs,one needs good [(m-1)/m] rational approximants to z-1/2 on the union of a positive and a negative real line segment.
We present a method for recontructing the Schroedinger potential from Dirichlet to Neumann map measurements at the boundary of a 2D region.Our method relies on the Liouville identity relating the cond