A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations

Lin, Xue-lei; Ng, Kwok Po; Sun, Hai‐Wei

doi:10.4208/nmtma.2018.s09

Cited by 16 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Ref. 7 Lin et al have proposed the SEP preconditioner for linear systems, arising from discretization of time-space fractional Caputo-Riesz diffusion equation, with such structure so that the Krylov subspace method for these preconditioned linear systems converges fast and independently on both temporal and spatial mesh parameters. Sheng et al 8 proposed a hybrid spectral element method for fractional two-point boundary value problem (FBVPs) involving both Caputo and Riemann-Liouville (RL) fractional derivatives.…”

Section: Andmentioning

confidence: 99%

A numerical framework for the approximate solution of fractional tumor-obesity model

Arshad

Băleanu

Defterli

et al. 2019

Int. J. Model. Simul. Sci. Comput.

View full text Add to dashboard Cite

In this paper, we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and Caputo-Fabrizio (CF). Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed. Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models. We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.

show abstract

Section: Andmentioning

confidence: 99%

A numerical framework for the approximate solution of fractional tumor-obesity model

Arshad

Băleanu

Defterli

et al. 2019

Int. J. Model. Simul. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…Nguyen et al settled a terminal value problem for time fractional diffusion equation by using regularization [26]. In addition, more researchers have found other numerical schemes such as the finite element method and others [12,15,18,33,35,37,46,52]. Zhou et al structured a weak Galerkin finite element method for multi-term time fractional diffusion equations [52].…”

Section: Introductionmentioning

confidence: 99%

“…Zhou et al structured a weak Galerkin finite element method for multi-term time fractional diffusion equations [52]. Lin et al obtained a separable freconditioner for time-space fractional Caputo-Riesz diffusion equations [18]. Sheng and Shen proposed a space-time Petrov-Galerkin spectral method for time fractional diffusion equation [33].…”

Section: Introductionmentioning

confidence: 99%

High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

Jiang

2020

Adv Differ Equ

View full text Add to dashboard Cite

Based on an L1 interpolation operator, a new high-order compact finite volume scheme is derived for the 2D multi-term time fractional sub-diffusion equation. It is shown that the difference scheme is unconditionally convergent and stable in $L_{\infty }$ L ∞ -norm. The convergence order is $O(\tau ^{2-\alpha }+h_{1}^{4}+h_{2}^{4})$ O ( τ 2 − α + h 1 4 + h 2 4 ) , where τ is the temporal step size and $h_{1}$ h 1 is the spatial step size in one direction, $h_{2}$ h 2 is the spatial step size in another direction. Two numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

show abstract

“…This scheme efficiently reduces the computational storage and cost for solving the time FDEs. Although there are many studies on the space/time FDEs, numerical studies on space-time FDEs are still not extensive, the readers are suggested to see [11,[38][39][40] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

Yong-LiangZhao¹

2019

EAJAM

View full text Add to dashboard Cite

An implicit finite difference scheme based on the L2-1 σ formula is presented for a class of one-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability and convergence of this scheme are proved rigorously by the discrete energy method, and the optimal convergence order in the L 2 -norm is O(τ 2 + h 2 ) with time step τ and mesh size h. Then, the same measure is exploited to solve the two-dimensional case of this problem and a rigorous theoretical analysis of the stability and convergence is carried out. Several numerical simulations are provided to show the efficiency and accuracy of our proposed schemes and in the last numerical experiment of this work, three preconditioned iterative methods are employed for solving the linear system of the two-dimensional case.

show abstract

A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations

Cited by 16 publications

References 0 publications

A numerical framework for the approximate solution of fractional tumor-obesity model

A numerical framework for the approximate solution of fractional tumor-obesity model

High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

Contact Info

Product

Resources

About