Journal ArticleDOI
Finite difference methods for the time fractional diffusion equation on non-uniform meshes
TLDR
The finite difference approximation of Caputo derivative on non-uniform meshes is investigated and a semi-discrete scheme is obtained and the unconditional stability and H^1 norm convergence are proved.About:
This article is published in Journal of Computational Physics.The article was published on 2014-05-01. It has received 226 citations till now. The article focuses on the topics: Finite difference method & Finite difference coefficient.read more
Citations
More filters
Journal ArticleDOI
A new difference scheme for the time fractional diffusion equation
TL;DR: A new difference analog of the Caputo fractional derivative (called the L 2 - 1 σ formula) is constructed and some difference schemes generating approximations of the second and fourth order in space and the second order in time for the time fractional diffusion equation with variable coefficients are considered.
Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy
TL;DR: In this article, two fully discrete schemes are proposed for the time-fractional subdiffusion equation with space discretized by finite element method and time discretised by fractional linear multistep methods.
Journal ArticleDOI
Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview
TL;DR: In this article, a concise overview on numerical schemes for the sub-diffusion model with nonsmooth problem data is given, which are important for the numerical analysis of many problems arising in optimal control, inverse problems and stochastic analysis.
Journal ArticleDOI
A new Rabotnov fractional‐exponential function‐based fractional derivative for diffusion equation under external force
Journal ArticleDOI
Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
Changpin Li,Qian Yi,An Chen +2 more
TL;DR: In this article, finite difference methods with non-uniform meshes for solving nonlinear fractional differential equations are presented, where the non-equidistant stepsize is non-decreasing and the rectangle formula and trapezoid formula are proposed based on theNon- uniform meshes.
References
More filters
Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Journal ArticleDOI
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
TL;DR: In this article, the authors consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder, and illustrate the theoretical models by describing many physical situations where anomalous (non-Brownian) diffusion laws have been observed or could be observed.
Book
The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order
Keith B. Oldham,Jerome Spanier +1 more
TL;DR: In the beginning, when having significantly cash, why don't you attempt to acquire something basic in the beginning? That's something that will guide you to understand even more in the region of the globe, experience, some places, history, amusement, and a lot more as discussed by the authors.
Journal ArticleDOI
Finite difference/spectral approximations for the time-fractional diffusion equation
Yumin Lin,Chuanju Xu +1 more
TL;DR: It is proved that the full discretization is unconditionally stable, and the numerical solution converges to the exact one with order O(@Dt^2^-^@a+N^- ^m), where @Dt,N and m are the time step size, polynomial degree, and regularity of the exact solution respectively.