A Fourier method for the fractional diffusion equation describing sub-diffusion

By Chang-Ming Chen, Fawang Liu, Ian L Turner, Vo Anh. Journal of Computational Physics, 2007

375 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/63f4bc228b40d1f9c3e9f83bda0fbf647e1028e9

How researchers see this paper

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

In Applied Mathematics

1. Mingrong Cui
2. Changpin Li
3. Fanhai Zeng
4. Ian L Turner
5. Zhibo Wang
6. Fawang Liu
7. Seakweng Vong
8. Ying Zhang

In Modeling and Simulation

1. Changpin Li
2. Ian L Turner
3. Fawang Liu
4. Fanhai Zeng
5. Mingrong Cui
6. YangQuan Chen
7. Zhibo Wang
8. Jianxiong Cao

In Numerical Analysis

1. Changpin Li
2. Ian L Turner
3. Fawang Liu
4. Fanhai Zeng
5. Mingrong Cui
6. YangQuan Chen
7. Zhibo Wang
8. Jianxiong Cao

Citations in the corpus

• Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, neutral): “, [4], [10], [36], [32], [120], [60], [79], so, if this was the only case one is interested in, it would not be worthwhile adding yet another method to this set.”
• The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation (2013, methodology): “[7] developed an implicit algorithm for the subdiffusion equation with first-order accuracy in time.”
• Local discontinuous Galerkin methods for fractional diffusion equations (2013, positive): “While these observations both suggest that it may be worth considering higher order accurate formulation as attractive alternatives, there appears to be very limited work in that direction with a few notable exceptions being [5,16,17] in which spectral methods are used to discretize classical space ”
• Compact finite difference method for the fractional diffusion equation (2009, methodology): “We will prove that the compact finite re is a typo in [7], P1 l1⁄40kl should be zero, as klðl 1⁄4 0;1; .”
• High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II) (2015, methodology): “We further discuss the stability of the proposed scheme by the Fourier method [3].”
• Inverse source problem for a fractional diffusion equation (2011, methodology): “For the sake of completeness, we also mention that numerical approaches were proposed by many researchers, such as Sun et al [32] and Chen et al [6] which adopted a finite difference method, and Lin [15] employed a finite/spectral method and Brunner [4] solved 2D fractional subdiffusion problems by ”
• Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation (2013, methodology): “Numerical methods for the modified anomalous fractional sub-diffusion equation and the diffusion-wave equation have been considered by many authors, one may refer to [6]–[17] and the references therein.”