Finite difference methods for fractional dispersion equations

Su, Lijuan; Wang, Wenqia; Xu, Qiuyan

doi:10.1016/j.amc.2010.04.060

Cited by 49 publications

(35 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of the major advantages of the fractional derivatives is that they can be considered as a super set of integer-order derivatives. Thus, fractional derivatives have the potential to accomplish what integer-order derivatives cannot [3]. A history of the development of fractional differential operators can be found in [4,5].…”

Section: Introductionmentioning

confidence: 99%

A tau approach for solution of the space fractional diffusion equation

Saadatmandi

Dehghan

2011

Computers & Mathematics with Applications

200

111

View full text Add to dashboard Cite

a b s t r a c tFractional differentials provide more accurate models of systems under consideration. In this paper, approximation techniques based on the shifted Legendre-tau idea are presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain. The fractional derivatives are described in the Caputo sense. The technique is derived by expanding the required approximate solution as the elements of shifted Legendre polynomials. Using the operational matrix of the fractional derivative the problem can be reduced to a set of linear algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use.

show abstract

Section: Introductionmentioning

confidence: 99%

A tau approach for solution of the space fractional diffusion equation

Saadatmandi

Dehghan

2011

Computers & Mathematics with Applications

200

111

View full text Add to dashboard Cite

show abstract

“…In another hand, if υ + αμ α 1, the fractional EUFDM is stable [25]. That is to say, if we note κ = υ + αμ α , when κ 1, the fractional EUFDM is stable.…”

Section: Comparison With the Fractional Explicit Upwind Finite Differmentioning

confidence: 94%

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

Wang

2011

Applied Numerical Mathematics

Self Cite

View full text Add to dashboard Cite

“…In recent decades, the Chebyshev polynomials are one of the most useful polynomials which are suitable in numerical analysis including polynomial approximation, integral and differential equations and spectral methods for partial differential equations and fractional order differential equations (see, Canuto et al, 2006;Dalir and Bashour, 2010;Mason and Handscomb, 2003;Scalas et al, 2003;Su et al, 2010;Sousa, 2011;Tadjeran et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

On the numerical solution of space fractional order diffusion equation via shifted Chebyshev polynomials of the third kind

Sweilam

Nagy

El‐Sayed

2016

Journal of King Saud University - Science

View full text Add to dashboard Cite

KEYWORDSSpace fractional order diffusion equation; Caputo derivative; Chebyshev collocation method; Finite difference method; Chebyshev polynomials of the third kind Abstract In this paper, we propose a numerical scheme to solve space fractional order diffusion equation. Our scheme uses shifted Chebyshev polynomials of the third kind. The fractional differential derivatives are expressed in terms of the Caputo sense. Moreover, Chebyshev collocation method together with the finite difference method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical approximations performed by the proposed method are presented and compared with the results obtained by other numerical methods. The results reveal that our method is a simple and effective numerical method. ª 2015 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

show abstract

Finite difference methods for fractional dispersion equations

Cited by 49 publications

References 18 publications

A tau approach for solution of the space fractional diffusion equation

A tau approach for solution of the space fractional diffusion equation

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

On the numerical solution of space fractional order diffusion equation via shifted Chebyshev polynomials of the third kind

Contact Info

Product

Resources

About