2022/09/01 by Xiangyi Peng, Peng, Xiangyi, Wenlin Qiu +2
Mathematics · Physics and Astronomy · #Applied mathematics #Burgers' equation #Compact finite difference #Compact space #Differential Equations and Numerical Methods #Discretization #FOS: Mathematics #Fractional Differential Equations Solutions #Fractional calculus #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Norm (philosophy) #Numerical Analysis (math.NA) #Operator (biology) #Partial differential equation #Physics #Pointwise
paper · pdf · doi:10.48550/arxiv.2209.00217
openalex publication_date 2022/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel fourth-order compact difference scheme is constructed for the mixed-type time-fractional Burgers' equation, from which L1-discretization formula is employed to deal with the terms of fractional derivative, and the nonlinear convection term is discretized by nonlinear compact difference operator. Then a fully discrete compact difference scheme can be established by approximating spatial second-order derivative with classic compact difference formula. The convergence and stability are rigorously proved in the L∞-norm by the energy argument and mathematical induction. Finally, several numerical experiments are provided to verify the theoretical analysis.