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Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations

Author

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  • X. Wang
  • F. Liu
  • X. Chen

Abstract

We derive and analyze second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations (RSDO-ADE) in one-dimensional (1D) and two-dimensional (2D) cases, respectively. Firstly, we discretize the Riesz space distributed-order advection-dispersion equations into multiterm Riesz space fractional advection-dispersion equations (MT-RSDO-ADE) by using the midpoint quadrature rule. Secondly, we propose a second-order accurate implicit numerical method for the MT-RSDO-ADE. Thirdly, stability and convergence are discussed. We investigate the numerical solution and analysis of the RSDO-ADE in 1D case. Then we discuss the RSDO-ADE in 2D case. For 2D case, we propose a new second-order accurate implicit alternating direction method, and the stability and convergence of this method are proved. Finally, numerical results are presented to support our theoretical analysis.

Suggested Citation

  • X. Wang & F. Liu & X. Chen, 2015. "Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-14, November.
    • Handle: RePEc:hin:jnlamp:590435
    DOI: 10.1155/2015/590435
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    Cited by:

    1. M. Luísa Morgado & Magda Rebelo & Luís L. Ferrás, 2021. "Stable and Convergent Finite Difference Schemes on NonuniformTime Meshes for Distributed-Order Diffusion Equations," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    2. Adán J. Serna-Reyes & Jorge E. Macías-Díaz, 2021. "A Mass- and Energy-Conserving Numerical Model for a Fractional Gross–Pitaevskii System in Multiple Dimensions," Mathematics, MDPI, vol. 9(15), pages 1-31, July.
    3. Yu, Qiang & Turner, Ian & Liu, Fawang & Vegh, Viktor, 2022. "The application of the distributed-order time fractional Bloch model to magnetic resonance imaging," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    4. Joel Alba-Pérez & Jorge E. Macías-Díaz, 2019. "Analysis of Structure-Preserving Discrete Models for Predator-Prey Systems with Anomalous Diffusion," Mathematics, MDPI, vol. 7(12), pages 1-31, December.
    5. Jorge E. Macías-Díaz & Nuria Reguera & Adán J. Serna-Reyes, 2021. "An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    6. Adán J. Serna-Reyes & Jorge E. Macías-Díaz & Nuria Reguera, 2021. "A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    7. Jorge E. Macías-Díaz, 2019. "Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
    8. Martínez, Romeo & Macías-Díaz, Jorge E. & Sheng, Qin, 2022. "A nonlinear discrete model for approximating a conservative multi-fractional Zakharov system: Analysis and computational simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 1-21.

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