In this paper, we focus on the study of the Crank–Nicolson finite difference (CNFD) scheme for the Riesz space fractional-order parabolic-type sine-Gordon equation (RSFOPTSGE). For this purpose, we first establish the CNFD scheme for RSFOPTSGE. Then, we discuss the existence, uniqueness, stability, and convergence of the CNFD solutions. Finally, we supply a numerical experiment to validate the correctness of theoretical results. This indicates that the CNFD scheme is very effective for solving RSFOPTSGE.
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Zhou et al. (2018) studied this question.