Solving KdV equation with finite difference optimized compact scheme for first- and third-derivatives
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If you find it useful you can cite the original article:
@Article{Ashwin2015,
author="Ashwin, V. M.
and Saurabh, K.
and Sriramkrishnan, M.
and Bagade, P. M.
and Parvathi, M. K.
and Sengupta, Tapan K.",
title="KdV Equation and Computations of Solitons: Nonlinear Error Dynamics",
journal="Journal of Scientific Computing",
year="2015",
month="Mar",
day="01",
volume="62",
number="3",
pages="693--717",
abstract="Here we have developed new compact and hybrid schemes for the
solution of KdV equation. These schemes for the third derivative have been
analyzed in the spectral plane for their resolution and compared with another
scheme in the literature. Furthermore the developed schemes have been used to
solve a model linear dispersion equation. The error dynamics equation has been
developed for this model equation. Despite the linearity of the model equation,
one can draw conclusions for error dynamics of nonlinear differential
equations. The developed compact scheme has been found to be quite accurate in
solving KdV equation. One- and two-soliton cases have been reported to
demonstrate the above.",
issn="1573-7691",
doi="10.1007/s10915-014-9875-4",
url="https://doi.org/10.1007/s10915-014-9875-4"
}The published version can be found here.