TY - JOUR
T1 - High Order Finite Difference/Spectral Methods to a Water Wave Model with Nonlocal Viscosity
AU - Hasan , Mohammad Tanzil
AU - Xu , Chuanju
JO - Journal of Computational Mathematics
VL - 4
SP - 580
EP - 605
PY - 2020
DA - 2020/04
SN - 38
DO - http://doi.org/10.4208/jcm.1902-m2017-0280
UR - https://global-sci.org/intro/article_detail/jcm/16464.html
KW - Water waves, Nonlocal viscosity, Finite difference, Spectral method, Convergence order, Decay rate.
AB - <p style="text-align: justify;">In this paper, efficient numerical schemes are proposed for solving the water wave model
with nonlocal viscous term that describe the propagation of surface water wave. By using
the Caputo fractional derivative definition to approximate the nonlocal fractional operator,
finite difference method in time and spectral method in space are constructed for the
considered model. The proposed method employs known 5/2 order scheme for fractional
derivative and a mixed linearization for the nonlinear term. The analysis shows that
the proposed numerical scheme is unconditionally stable and error estimates are provided
to predict that the second order backward differentiation plus 5/2 order scheme converges
with order 2 in time, and spectral accuracy in space. Several numerical results are provided
to verify the efficiency and accuracy of our theoretical claims. Finally, the decay rate of
solutions is investigated.</p>