A pseudo-spectral splitting method for linear dispersive problems with transparent boundary conditions

The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital allow waves leave (or even re-enter) the, necessarily finite, computational To obtain efficient numerical scheme we discretize space using spectral method. This allows us drastically reduce number grid points required for given accuracy. Applying fully implicit time integrator, however, would require invert full matrices. addressed by performing operator splitting and only treating third order differential operator, stemming from part, implicitly; approach can also be interpreted as implicit–explicit scheme. However, fact that non-homogeneous depend implicitly solution presents significant obstacle splitting/pseudo-spectral investigated here. We show how overcome these difficulties demonstrate proposed simulations.