High order schemes for the tempered fractional diffusion equations
type: Item
instance of: scholarly article
title: High order schemes for the tempered fractional diffusion equations
zbMATH Open document ID: 1347.65136
author: Can Li
author: Weihua Deng
published in: Advances in Computational Mathematics
publication date: 2016-06-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1402.0064
review text: The authors study the tempered fractional diffusion equations. The high-order schemes for this system are designed by using Crank-Nicolson discretization in time, the tempered fractional calculus and the Grunwald type difference in space. The stability and convergence of the new derived numerical methods are presented.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6592756
zbMATH Keywords: tempered fractional diffusion equation
zbMATH Keywords: tempered Grunwald difference
zbMATH Keywords: Crank-Nicolson discretization
MaRDI profile type: Publication
OpenAlex ID: W2118072570
arXiv ID: 1402.0064
cites work: Tempered stable Lévy motion and transient super-diffusion
cites work: Decomposition of an Integral Operator by Use of Mikusiński Calculus
cites work: On distributions of functionals of anomalous diffusion paths
cites work: Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
cites work: Numerical algorithms for the forward and backward fractional Feynman-Kac equations
cites work: Classroom Note:Calculation of Weights in Finite Difference Formulas
cites work: Q5689624
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Q3141895
cites work: Q4115628
cites work: Numerical methods for the solution of partial differential equations of fractional order.
cites work: Numerical solution of the space fractional Fokker-Planck equation.
cites work: A comparison of numerical solutions of fractional diffusion models in finance
cites work: The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
cites work: Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy Flight
cites work: Finite difference approximations for fractional advection-dispersion flow equations
cites work: Stochastic models for fractional calculus
cites work: Riesz potential operators and inverses via fractional centred derivatives
cites work: Multigrid method for fractional diffusion equations
cites work: Q3410604
cites work: A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
cites work: A class of second order difference approximations for solving space fractional diffusion equations
cites work: Q4947421
cites work: A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
cites work: A series of high-order quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives
DOI: 10.1007/S10444-015-9434-Z
description: scientific article