Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Numerical solution of the space fractional Fokker-Planck equation
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Finite difference methods for two-dimensional fractional dispersion equation
Journal of Computational Physics
Short memory principle and a predictor-corrector approach for fractional differential equations
Journal of Computational and Applied Mathematics
Some noises with spectrum, a bridge between direct current and white noise
IEEE Transactions on Information Theory
Numerical simulation of blowup in nonlocal reaction-diffusion equations using a moving mesh method
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Proceedings of the 12th annual conference companion on Genetic and evolutionary computation
Numerical simulations of 2D fractional subdiffusion problems
Journal of Computational Physics
Explicit and implicit finite difference schemes for fractional Cattaneo equation
Journal of Computational Physics
Modeling and numerical analysis of fractional-order Bloch equations
Computers & Mathematics with Applications
On the use of matrix functions for fractional partial differential equations
Mathematics and Computers in Simulation
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Numerical analysis and physical simulations for the time fractional radial diffusion equation
Computers & Mathematics with Applications
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Journal of Scientific Computing
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Jacobian-predictor-corrector approach for fractional differential equations
Advances in Computational Mathematics
Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
Journal of Scientific Computing
Hi-index | 31.48 |
Anomalous diffusion is one of the most ubiquitous phenomena in nature, and it is present in a wide variety of physical situations, for instance, transport of fluid in porous media, diffusion of plasma, diffusion at liquid surfaces, etc. The fractional approach proved to be highly effective in a rich variety of scenarios such as continuous time random walk models, generalized Langevin equations, or the generalized master equation. To investigate the subdiffusion of anomalous diffusion, it would be useful to study a time fractional Fokker-Planck equation. In this paper, firstly the time fractional, the sense of Riemann-Liouville derivative, Fokker-Planck equation is transformed into a time fractional ordinary differential equation (FODE) in the sense of Caputo derivative by discretizing the spatial derivatives and using the properties of Riemann-Liouville derivative and Caputo derivative. Then combining the predictor-corrector approach with the method of lines, the algorithm is designed for numerically solving FODE with the numerical error O(k^m^i^n^{^1^+^2^@a^,^2^})+O(h^2), and the corresponding stability condition is got. The effectiveness of this numerical algorithm is evaluated by comparing its numerical results for @a=1.0 with the ones of directly discretizing classical Fokker-Planck equation, some numerical results for time fractional Fokker-Planck equation with several different fractional orders are demonstrated and compared with each other, moreover for @a=0.8 the convergent order in space is confirmed and the numerical results with different time step sizes are shown.