Spectral stability analysis of a new difference scheme of time fractional advection dispersion equations

Karatay, Ibrahim; Kale, Nurdane; Erguner, Serife R. Bayramoglu

doi:10.12988/ijma.2014.410325

Cited by 6 publications

(9 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…substituting (7), (8) and (15) in (4), we obtain the following implicit numerical scheme: l = 1, . .…”

Section: Numerical Schemementioning

confidence: 99%

“…In order to prove the convergence order of the numerical scheme, let us first note that taking into account (7), (8) and (15), the solution of (4)-(6) satisfies: …”

Section: Convergence Of the Numerical Schemementioning

confidence: 99%

“…We assume that g, f , φ 0 and φ L are continuous functions in their respective domains and we assume further that k(x, t) ≥ 0 and v(x, t) ≥ 0, for all x ∈ [0, L], t ∈ (0, T ], so that the "fluid" moves from the left to the right. TFADEs with an additional velocity field and under the influence of an external force field arise in many physical models where anomalous dispersion occurs [7][8][9][10]. Finite difference schemes are the most common for the numerical solution of TFADEs, and usually they are first-order accurate with respect to time and obtained via discretization of the problem in uniform meshes (see for example [10] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical modelling transient current in the time-of-flight experiment with time-fractional advection-diffusion equations

Morgado¹,

Morgado

2015

J Math Chem

View full text Add to dashboard Cite

In this work we report the development of an implicit finite difference numerical method for the one space dimension time-fractional advection-diffusion equation, on a bounded domain, to model the transient electrical current of the time of flight experiment of disordered (e.g. organic) semiconductors. Some numerical experiments and simulation of experimental data are carried out showing that the presented model describes accurately the transient electrical current.

show abstract

“…substituting (7), (8) and (15) in (4), we obtain the following implicit numerical scheme: l = 1, . .…”

Section: Numerical Schemementioning

confidence: 99%

“…In order to prove the convergence order of the numerical scheme, let us first note that taking into account (7), (8) and (15), the solution of (4)-(6) satisfies: …”

Section: Convergence Of the Numerical Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical modelling transient current in the time-of-flight experiment with time-fractional advection-diffusion equations

Morgado¹,

Morgado

2015

J Math Chem

View full text Add to dashboard Cite

show abstract

“…We can also mention the implicit difference method based on the shifted Grünwald-Letnikov approximation [36], transformation of fractional differential equation into a system of ordinary differential equation [37], the random walk algorithms [38,39], the spectral regularization method [52], the Crank-Nicholson difference scheme [53], Adomian's decomposition [50], a spatial and temporal discretization [64], the fractional variational iteration method [54], the homotopy perturbation method [51,63,72] and the Jacobi collocation method [73].…”

Section: Introductionmentioning

confidence: 99%

Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation

Povstenko

Kyrylych

2017

Entropy

View full text Add to dashboard Cite

Two approaches resulting in two different generalizations of the space-time-fractional advection-diffusion equation are discussed. The Caputo time-fractional derivative and Riesz fractional Laplacian are used. The fundamental solutions to the corresponding Cauchy and source problems in the case of one spatial variable are studied using the Laplace transform with respect to time and the Fourier transform with respect to the spatial coordinate. The numerical results are illustrated graphically.

show abstract

“…In [12,13], the Crank-Nicholson method was applied directly to obtain a numerical solution for the time fractional advection dispersion equations with Riemann-Liouville derivative.…”

Section: Introductionmentioning

confidence: 99%

A new difference scheme for time fractional heat equations based on the Crank-Nicholson method

Karatay

Kale

Bayramoglu

2013

fcaa

Self Cite

View full text Add to dashboard Cite

In this paper, we consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with the Caputo derivative of order α, where 0 < α < 1. The main purpose of this work is to extend the idea on the Crank-Nicholson method to the time-fractional heat equations. By the method of the Fourier analysis, we prove that the proposed method is stable and the numerical solution converges to the exact one with the order O(τ 2−α + h 2 ), conditionally. Numerical experiments are carried out to support the theoretical claims.MSC 2010 : 65M12, 65M06

show abstract

Spectral stability analysis of a new difference scheme of time fractional advection dispersion equations

Cited by 6 publications

References 11 publications

Numerical modelling transient current in the time-of-flight experiment with time-fractional advection-diffusion equations

Numerical modelling transient current in the time-of-flight experiment with time-fractional advection-diffusion equations

Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation

A new difference scheme for time fractional heat equations based on the Crank-Nicholson method

Contact Info

Product

Resources

About