A direct O(N log2 N) finite difference method for fractional diffusion equations

By Hong Wang, Kaixin Wang, Treena Sircar. Journal of Computational Physics, 2010

314 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c37b77bf6c2abef07c3b4ac59cafcf86b9f376a8

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. M. A. Zaky
5. Ali H. Bhrawy
6. Vo Anh
7. Fanhai Zeng
8. Kevin Burrage

In Numerical Analysis

1. Changpin Li
2. Fawang Liu
3. Ian L Turner
4. M. A. Zaky
5. Vo Anh
6. Ali H. Bhrawy
7. Fanhai Zeng
8. Kevin Burrage

Citations in the corpus

• A Fast Finite Difference Method for Three-Dimensional Time-Dependent Space-Fractional Diffusion Equations with Fractional Derivative Boundary Conditions (2017, background): “It was shown in [29] that T α,N1 ũk, j can be evaluated in O(N1 log N1) operations.”
• A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation (2014, methodology): “Some fast solution techniques were developed in [43, 44, 45, 40, 41] to solve the space fractional differential equations, in which the fractional derivative operators are discretized by the finite difference methods that yield a coefficient matrix with special structures.”
• A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations (2015, methodology): “Several numerical methods have been proposed in the last few years for solving SFADE such that finite difference method [17–20], finite volume method [21], random walk method [22], random walk particle tracking method [23,24],”
• The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation (2013, methodology): “Similar to the numerical methods for the classical differential equations, there also exist finite difference methods [3, 10, 12, 13, 20, 24, 26, 27, 31, 34, 51, 52, 54, 55, 62], finite element methods (FEMs) [16, 48, 59, 61], and spectral methods [6, 25, 28] for numerically solving the FDEs.”
• Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations (2015, unknown): “For any mesh functions g = { g k | 0 ≤ k ≤ N } defined on Ω t , the following inequality holds:”