Numerical solution of the space fractional Fokker-Planck equation

By Fawang Liu, Vo Anh, Ian L Turner. 2004

748 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4d6252845fa8904de42a72b279a9f4afd9a26b56

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Citations in the corpus

A second-order accurate numerical approximation for the fractional diffusion equation (2006, methodology): “Several different first-order accurate numerical methods to solve fractional diffusion equations have been presented before [3,4,6,7,9,10].”
TEMPERED FRACTIONAL CALCULUS (2015, methodology): “A wide variety of effective numerical methods have been developed to solve fractional diffusion equations, see for example [18,21,32–34,56,64,68].”
Exact Solution of Some Linear Fractional Differential Equations by Laplace Transform (2013, methodology): “During the last decades, several methods have been used to solve fractional differential equations, fractional partial differential equations, fractional integro-differential equations and dynamic systems containing fractional derivatives, such as Adomian’s decomposition method [9–13], He’s variatio”
A characteristic difference method for the variable-order fractional advection-diffusion equation (2013, neutral): “[15], Schumer et al.”
Implicit finite difference approximation for time fractional diffusion equations (2008, methodology): “For the numerical solution of the space fractional diffusion equations (SFDE), finite elements together with the method of lines [3], explicit and implicit finite difference methods, [7,4,8], have been proposed.”
A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions (2018, methodology): “[11] transformed the space fractional Fokker-Planck equation into a system of ordinary differential equations (method of lines), which was then solved using backward differentiation formulas.”
Variational iteration method for the Burgers' flow with fractional derivatives—New Lagrange multipliers (2013, neutral): “Some numerical methods [1–6] and analytical methods [7–12] have been developed for fractional differential equations (FDEs).”
Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation (2007, methodology): “simulate the fractional Fokker-Planck equation [18, 19 ].”
A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations (2015, methodology): “The space fractional advection–dispersion equation (SFADE) is used to describe the transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns [14,15] and it is also proved as a benefit tool to model the transport of passive tracers carried”
New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation (2008, methodology): “[12, 13] transformed the space fractional partial differential equation into a system of ordinary differential equations (method of lines) that was then solved using backward differentiation formulas.”
Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation (2010, background): “The work on the numerical solution of the nonlinear fractional Fokker-Planck equation is relatively sparse [8, 25].”