1304.4213 (Paolo Marconcini et al.)

Sinc-based method for a high-precision solution in the direct space of
wave equations with periodic boundary conditions    [PDF]

Paolo Marconcini, Demetrio Logoteta, Massimo Macucci

Direct-space finite-difference approaches usually require, to achieve a similar accuracy, the solution of larger algebraic problems with respect to those resulting from a formulation based on the Fourier transform in the reciprocal space. This is the result of errors that are introduced in the treatment of the derivatives with the application of direct-space discretization formulas. Here we propose an approach, based on a particular set of basis functions, that allows us to obtain an exact treatment of the derivatives in the direct space and that is equivalent to the solution in the reciprocal space. We apply this method to the numerical solution of the Dirac equation in an armchair graphene nanoribbon with a potential varying only in the transverse direction.

View original: http://arxiv.org/abs/1304.4213