A two-level linearized scheme for two-dimensional Riesz space fractional nonlinear advection-dispersion equations

Wenwen Shan; Tao Wang

doi:10.1117/12.2692000

23 August 2023 A two-level linearized scheme for two-dimensional Riesz space fractional nonlinear advection-dispersion equations

Wenwen Shan, Tao Wang

Author Affiliations +

Proceedings Volume 12784, Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023); 127841C (2023) https://doi.org/10.1117/12.2692000
Event: 2023 2nd International Conference on Applied Statistics, Computational Mathematics and Software Engineering (ASCMSE 2023), 2023, Kaifeng, China

Abstract

Nonlinear Riesz space fractional advection-dispersion equations (SFADEs) find widespread applications in many fields, and numerical solutions are the primary means of solving such equations due to the complexity of nonlinear problems. A majority of the existing numerical techniques for solving nonlinear equations are based on three-level schemes, thereby leading to increased computational overheads and theoretical challenges. A novel approach is developed to solve two-dimensional nonlinear Riesz SFADEs, which employs a two-level linearized finite difference method and incorporates state-of-the-art linearization techniques. The proposed approach involves using the Crank-Nicolson approach to process the time component and approximating the Riesz space fractional derivative using the weighted and shifted Grünwald difference (WSGD) formula. The resulting difference scheme is observed to exhibit second-order convergence in both temporal and spatial coordinates. The efficiency and accuracy of the proposed method are confirmed by conducting numerical experiments.

Citation Download Citation

Wenwen Shan and Tao Wang "A two-level linearized scheme for two-dimensional Riesz space fractional nonlinear advection-dispersion equations", Proc. SPIE 12784, Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023), 127841C (23 August 2023); https://doi.org/10.1117/12.2692000

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