Numerical methods for fractional partial differential equations
Top Cited Papers
- 3 July 2017
- journal article
- research article
- Published by Taylor & Francis Ltd in International Journal of Computer Mathematics
- Vol. 95 (6-7), 1048-1099
- https://doi.org/10.1080/00207160.2017.1343941
Abstract
In this review paper, we are mainly concerned with the finite difference methods, the Galerkin finite element methods, and the spectral methods for fractional partial differential equations (FPDEs), which are divided into the time-fractional, space-fractional, and space-time-fractional partial differential equations (PDEs). Besides, fast algorithms for the FPDEs are included in order to stimulate more efficient algorithms for high-dimensional FPDEs.Keywords
Funding Information
- National Natural Science Foundation of China (11372170, 11671251, 11632008)
This publication has 183 references indexed in Scilit:
- A fast finite difference method for three-dimensional time-dependent space-fractional diffusion equations and its efficient implementationJournal of Computational Physics, 2013
- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operatorComputers & Mathematics with Applications, 2013
- Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic EquationsSIAM Journal on Numerical Analysis, 2013
- Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential EquationsSIAM Journal on Numerical Analysis, 2013
- Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion EquationsJournal of Scientific Computing, 2012
- Multigrid method for fractional diffusion equationsJournal of Computational Physics, 2012
- Finite element approximation for a modified anomalous subdiffusion equationApplied Mathematical Modelling, 2011
- A compact difference scheme for the fractional diffusion-wave equationApplied Mathematical Modelling, 2010
- Numerical methods for fractional partial differential equations with Riesz space fractional derivativesApplied Mathematical Modelling, 2010
- A fully discrete difference scheme for a diffusion-wave systemApplied Numerical Mathematics, 2006