@TechReport{ it:2013-007,
author = {Emil Kieri},
title = {Accelerated Convergence for {S}chr{\"o}dinger Equations
with Non-Smooth Potentials},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2013},
number = {2013-007},
month = apr,
abstract = {When numerically solving the time-dependent
Schr{\"o}dinger equation for the electrons in an atom or
molecule, the Coulomb singularity poses a challenge. The
solution will have limited regularity, and high-order
spatial discretisations, which are much favoured in the
chemical physics community, are not performing to their
full potential. By exploiting knowledge about the jumps in
the derivatives of the solution we construct a correction,
and show how this improves the convergence rate of Fourier
collocation from second to fourth order. This allows for a
substantial reduction in the number of grid points. The new
method is applied to the higher harmonic generation from
atomic hydrogen.}
}