Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation

By Fawang Liu, Pinghui Zhuang, Vo Anh, Ian L Turner, Kevin Burrage. Applied Mathematics and Computation, 2007

548 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f522c899f173ccfbf40fe22e512dbce2737c7302

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

1. Fawang Liu
2. Changpin Li
3. Ian L Turner
4. Vo Anh
5. Pinghui Zhuang
6. Fanhai Zeng
7. Kevin Burrage
8. Chang-Ming Chen

In Numerical Analysis

1. Fawang Liu
2. Changpin Li
3. Ian L Turner
4. Vo Anh
5. Pinghui Zhuang
6. Fanhai Zeng
7. Kevin Burrage
8. Chang-Ming Chen

Citations in the corpus

• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term (2009, background): “[17] con∗Received by the editors July 18, 2008; accepted for publication (in revised form) December 15, 2008; published electronically May 6, 2009.”
• Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation (2007, methodology): “[22] also investigated the stability and convergence of the difference methods for the space-time fractional advectiondiffusion equation.”
• Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation (2013, methodology): “Although the difference scheme has been discussed in the previous works [26, 29], we still give it here for completeness.”
• A Fourier method for the fractional diffusion equation describing sub-diffusion (2007, methodology): “Some numerical methods for solving the space or time, or time-space fractional partial difierential equations have been proposed [15],[16],[17], [18], [19], [20], [21], [22], [ 23 ], [24].”
• Time‐dependent fractional advection–diffusion equations by an implicit MLS meshless method (2011, methodology): “Hence, an adaptive analysis is easily achievable; they are usually more accurate than FDM and FEM due to the use of higher order meshless trial functions; and they are capable of solving complex problems that are difficult for the conventional FDM and FEM.”
• A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation (2014, methodology): “Up to now, there has been some work on numerical methods for FDEs, such as finite difference methods [12, 20, 26, 47], finite element methods [5, 6, 11, 14, 42], spectral methods [13, 15, 16], and so on [28, 29, 30].”
• Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method (2013, methodology): “[22] used explicit and implicit difference methods to solve spacetime fractional advection-dispersion equation and proved the stability and convergence of the methods.”
• The -Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey (2010, unknown): “[7, 8, 9], [20, 21], [29, 30], [71].”