A Conservative Difference Scheme for Space Fractional Klein-Gordon-Schrödinger Equations with a High-Degree Yukawa Interaction
Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.220418.300618
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 715–745
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Space fractional Klein-Gordon-Schrödinger equation conservative difference scheme convergence quantum subdiffusion local high oscillation.