A characteristic difference method for the transient fractional convection–diffusion equations

Su, Lijuan; Wang, Wenqia; Wang, Hong

doi:10.1016/j.apnum.2011.02.007

Cited by 27 publications

(11 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Qian et al presented the characteristic finite difference streamline diffusion method [6] and the characteristic variational multiscale method [7] for convection-dominated problems, respectively. Recently, Wang [8,9] and his coworkers extend characteristic FDM to fractional advection-diffusion equations. In problems with significant convection, these approaches of characteristics have much smaller time-truncation errors compared with the traditional FDM or FEM.…”

Section: Introductionmentioning

confidence: 98%

A block-centered characteristic finite difference method for convection-dominated diffusion equation

Zhai

Qian

GUI

et al. 2015

International Communications in Heat and Mass Transfer

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 98%

A block-centered characteristic finite difference method for convection-dominated diffusion equation

Zhai

Qian

GUI

et al. 2015

International Communications in Heat and Mass Transfer

View full text Add to dashboard Cite

“…For space fractional CDE, many researchers exploited the conventional shifted Grünwald discretization [9] and the implicit Euler (or Crank-Nicolson) time-step discretization for two-sided Riemman-Liouville fractional derivatives and the first order time derivative, respectively. Then they constructed many numerical treatments for space fractional CDE, refer to [9][10][11][12][13][14][15][16][17][18] and references therein for details. Later, Chen and Deng combined the second-order discretization with the Crank-Nicolson temporal discretization for producing the novel numerical methods, which archive the second order accuracy in both time and space for space fractional CDE [19,20].…”

Section: Introductionmentioning

confidence: 99%

Fast Iterative Method with a Second-Order Implicit Difference Scheme for Time-Space Fractional Convection–Diffusion Equation

Huang

et al. 2017

J Sci Comput

104

View full text Add to dashboard Cite

In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided weighted shifted Grünwald formulae is proposed with a discussion of the stability and convergence. We construct an implicit difference scheme (IDS) and show that it converges with second order accuracy in both time and space. Then, we develop fast solution methods for handling the resulting system of linear equation with the Toeplitz matrix. The fast Krylov subspace solvers with suitable circulant preconditioners are designed to deal with the resulting Toeplitz linear systems. * Each time level of these methods reduces the memory requirement of the proposed implicit difference scheme from O(N 2 ) to O(N ) and the computational complexity from O(N 3 ) to O(N log N ) in each iterative step, where N is the number of grid nodes. Extensive numerical example runs show the utility of these methods over the traditional direct solvers of the implicit difference methods, in terms of computational cost and memory requirements.

show abstract

“…Su et al . combining characteristic methods and fractional FDMs solved the two‐sided space‐fractional convection–diffusion equations. Also for more research works in this subject we refer the interested reader to .The outline of this paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

“…The authors of [60] presented a numerical scheme based on the collocation techniques for classes of TFCDEs with variable coefficients. Su et al [61] combining characteristic methods and fractional FDMs solved the two-sided space-fractional convection-diffusion equations. Also for more research works in this subject we refer the interested reader to [62,63].…”

Section: Introductionmentioning

confidence: 99%

The dual reciprocity boundary elements method for the linear and nonlinear two‐dimensional time‐fractional partial differential equations

Dehghan

Safarpoor

2016

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we apply the dual reciprocity boundary elements method for the numerical solution of two-dimensional linear and nonlinear time-fractional modified anomalous subdiffusion equations and time-fractional convection-diffusion equation. The fractional derivative of problems is described in the Riemann-Liouville and Caputo senses. We employ the linear radial basis function for interpolation of the nonlinear, inhomogeneous and time derivative terms. This method is improved by using a predictor-corrector scheme to overcome the nonlinearity which appears in the nonlinear problems under consideration. The accuracy and efficiency of the proposed schemes are checked by five test problems. The proposed method is employed for solving some examples in two dimensions on unit square and also in complex regions to demonstrate the efficiency of the new technique.

show abstract

A characteristic difference method for the transient fractional convection–diffusion equations

Cited by 27 publications

References 26 publications

A block-centered characteristic finite difference method for convection-dominated diffusion equation

A block-centered characteristic finite difference method for convection-dominated diffusion equation

Fast Iterative Method with a Second-Order Implicit Difference Scheme for Time-Space Fractional Convection–Diffusion Equation

The dual reciprocity boundary elements method for the linear and nonlinear two‐dimensional time‐fractional partial differential equations

Contact Info

Product

Resources

About