arrow
Volume 8, Issue 4
A Conservative Difference Scheme for Space Fractional Klein-Gordon-Schrödinger Equations with a High-Degree Yukawa Interaction

Junjie Wang, Aiguo Xiao & Chenxi Wang

East Asian J. Appl. Math., 8 (2018), pp. 715-745.

Published online: 2018-10

Export citation
  • Abstract

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.

  • AMS Subject Headings

65M06, 65M12, 35R11

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-8-715, author = {Junjie Wang, Aiguo Xiao and Chenxi Wang}, title = {A Conservative Difference Scheme for Space Fractional Klein-Gordon-Schrödinger Equations with a High-Degree Yukawa Interaction}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {4}, pages = {715--745}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.220418.300618}, url = {http://global-sci.org/intro/article_detail/eajam/12816.html} }
TY - JOUR T1 - A Conservative Difference Scheme for Space Fractional Klein-Gordon-Schrödinger Equations with a High-Degree Yukawa Interaction AU - Junjie Wang, Aiguo Xiao & Chenxi Wang 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 -

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.

Junjie Wang, Aiguo Xiao and Chenxi Wang. (2018). A Conservative Difference Scheme for Space Fractional Klein-Gordon-Schrödinger Equations with a High-Degree Yukawa Interaction. East Asian Journal on Applied Mathematics. 8 (4). 715-745. doi:10.4208/eajam.220418.300618
Copy to clipboard
The citation has been copied to your clipboard