@Article{CiCP-24-623,
author = {Bradley E. Treeby, Elliott S. Wise and B. T. Cox},
title = {Nonstandard Fourier Pseudospectral Time Domain (PSTD) Schemes for Partial Differential Equations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {3},
pages = {623--634},
abstract = {<p style="text-align: justify;">A class of nonstandard pseudospectral time domain (PSTD) schemes for
solving time-dependent hyperbolic and parabolic partial differential equations (PDEs)
is introduced. These schemes use the Fourier collocation spectral method to compute
spatial gradients and a nonstandard finite difference scheme to integrate forwards in
time. The modified denominator function that makes the finite difference time scheme
exact is transformed into the spatial frequency domain or k-space using the dispersion
relation for the governing PDE. This allows the correction factor to be applied
in the spatial frequency domain as part of the spatial gradient calculation. The derived
schemes can be formulated to be unconditionally stable, and apply to PDEs in
any space dimension. Examples of the resulting nonstandard PSTD schemes for several
PDEs are given, including the wave equation, diffusion equation, and convection-diffusion
equation.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0192},
url = {http://global-sci.org/intro/article_detail/cicp/12273.html}
}