Space-fractional advection-dispersion equations by the Kansa method

By Guofei Pang, Wen Chen, Zhuojia Fu. 2015

136 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

How researchers see this paper

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

In Mechanics of Materials

1. Lu Lu
2. Mark Ainsworth
3. G. Em Karniadakis
4. Mark M. Meerschaert
5. Guofei Pang
6. Xiaozhe Hu
7. Wei Cai
8. Xuan Zhao

In Modeling and Simulation

1. G. Em Karniadakis
2. Lu Lu
3. Zhiping Mao
4. Guofei Pang
5. Mark Ainsworth
6. Fangying Song
7. Wei Cai
8. Mamikon A. Gulian

In Numerical Analysis

1. G. Em Karniadakis
2. Mark Ainsworth
3. Zhiping Mao
4. Fangying Song
5. Lu Lu
6. Mark M. Meerschaert
7. Guofei Pang
8. Xiaozhe Hu

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “The first term on the right-hand side is a fractional Laplacian, which is defined in the sense of directional derivatives [22, 29]: (2.”
• What is the fractional Laplacian? A comparative review with new results (2018, methodology): “For 0 α 2 (the fractional Laplacians in which we are interested), the above derivation fails because the inverse Fourier transform of the symbol |ξ |α no longer exists, even as a distribution.”
• Adaptive finite element method for fractional differential equations using hierarchical matrices (2016, background): “However, as the size of the problem increases, the time required to solve the final system of equations increases considerably due to the nonlocality of the fractional differential operators [43, 23, 10, 11, 30, 9, 4, 36, 37, 40, 26].”