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

Abstract EN

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.