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• W4281696952 abstract "Based on quadratic and linear polynomial interpolation approximations and the Crank-Nicolson technique, a new second-order difference approximation method of the Caputo fractional derivative of order α∈(1,2) is proposed. This method is different from the known second-order methods, which is called the L2-1σ Crank-Nicolson method in this paper. Using the L2-1σ Crank-Nicolson method of the Caputo fractional derivative, a fully discrete L2-1σ Crank-Nicolson difference method for two-dimensional time-fractional wave equations with variable coefficients is developed. The unconditional stability and convergence of the method are rigorously proved. The optimal error estimates in the discrete L2-norm and H1-norm are obtained under a relatively weak regularity condition. The error estimates show that the method has the second-order convergence in both time and space for all α∈(1,2). In order to overcome the loss of the temporal convergence order caused by the stronger singularity of the exact solution at the initial time, a nonuniform L2-1σ Crank-Nicolson difference method is also developed on a class of general nonuniform time meshes. Numerical results confirm the theoretical convergence result. The effectiveness of the nonuniform method for non-smooth solutions with the stronger singularity at the initial time is tested on a class of initially graded time meshes." @default.
• W4281696952 created "2022-06-13" @default.
• W4281696952 creator A5036762034 @default.
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• W4281696952 date "2022-07-01" @default.
• W4281696952 modified "2023-09-27" @default.
• W4281696952 title "A second-order L2-1 Crank-Nicolson difference method for two-dimensional time-fractional wave equations with variable coefficients" @default.
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• W4281696952 doi "https://doi.org/10.1016/j.camwa.2022.05.018" @default.
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