TY - JOUR
T1 - A Conservative Difference Scheme for Space Fractional Klein-Gordon-Schrödinger Equations with a High-Degree Yukawa Interaction
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 715
EP - 745
PY - 2018
DA - 2018/10
SN - 8
DO - http://doi.org/10.4208/eajam.220418.300618
UR - https://global-sci.org/intro/article_detail/eajam/12816.html
KW - Space fractional Klein-Gordon-Schrödinger equation, conservative difference scheme, convergence, quantum subdiffusion, local high oscillation.
AB - <p style="text-align: justify;">A conservative finite difference scheme for nonlinear space fractional Klein-Gordon-Schrödinger
systems with high-degree Yukawa interaction is studied. We show
that the arising difference equations are uniquely solvable and approximate solutions
converge to the exact solution at the rate O ($τ^2+h^2$). Moreover, we prove that the scheme
can be decoupled and preserves the mass and energy conservation laws. Numerous
examples confirm theoretical results and demonstrate the efficiency of the scheme. They
also show the influence of the fractional order and the high-degree term coefficient on
the shape and the propagation velocity of solitary waves.</p>