Stabilized reduced order models for the advection–diffusion–reaction equation using operator splitting

Operator splitting for the KdV equation

We provide a new analytical approach to operator splitting for equations of the type ut = Au + B(u) where A is a linear operator and B is quadratic. A particular example is the Korteweg–de Vries (KdV) equation ut−uux +uxxx = 0. We show that the Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently regular.

First and second order operator splitting methods for the phase field crystal equation

Article history: Received 16 October 2014 Received in revised form 8 May 2015 Accepted 30 June 2015 Available online 3 July 2015

Operator Splitting Methods for the Wigner-poisson Equation

1. I n t r o d u c t i o n . In this paper we shall discuss operator splitting methods to discretize the linear Wigner equation and the coupled Wigner-Poisson system. The Wigner formalism, which represents a phase-space description of quantum mechanics, has in recent years a t t racted considerable at tent ion of solid s tate physicists for including quantum effects in the simulation of ul tra-...

Symplectic splitting operator methods for the time-dependent Schrodinger equation.

We present a family of symplectic splitting methods especially tailored to solve numerically the time-dependent Schrodinger equation. When discretized in time, this equation can be recast in the form of a classical Hamiltonian system with a Hamiltonian function corresponding to a generalized high-dimensional separable harmonic oscillator. The structure of the system allows us to build highly ef...

Higher-order operator splitting methods for deterministic parabolic equations