Ø´ÛŒÙˆØ§Ù†ÛŒØ§Ù†, Ø., Ø®Ø¯Ø§Ø¨Ù†Ø¯Ù‡ Ù„Ùˆ, Ø. (2016). A second-order accurate numerical approximation for two-sided fractional boundary value advection-diffusion problem. Theory of Approximation and Applications, (), -.

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Ø´ÛŒÙˆØ§Ù†ÛŒØ§Ù†, Ø., Ø®Ø¯Ø§Ø¨Ù†Ø¯Ù‡ Ù„Ùˆ, Ø. (2016). 'A second-order accurate numerical approximation for two-sided fractional boundary value advection-diffusion problem', Theory of Approximation and Applications, (), pp. -.

Ø´ÛŒÙˆØ§Ù†ÛŒØ§Ù†, Ø., Ø®Ø¯Ø§Ø¨Ù†Ø¯Ù‡ Ù„Ùˆ, Ø. A second-order accurate numerical approximation for two-sided fractional boundary value advection-diffusion problem. Theory of Approximation and Applications, 2016; (): -.

A second-order accurate numerical approximation for two-sided fractional boundary value advection-diffusion problem

Articles in Press, Accepted Manuscript , Available Online from 17 June 2016

^{}Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran

Abstract

Fractional order partial differential equations are generalization of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. An approach based on the classical Crank-Nicolson method combined with spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Stability, consistency, and convergence of the method are examined. It is shown that the fractional Crank-Nicolson method based on the shifted Gr"{u}nwald formula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solution for its order of convergence.

Fractional order partial differential equations are generalization of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. An approach based on the classical Crank-Nicolson method combined with spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Stability, consistency, and convergence of the method are examined. It is shown that the fractional Crank-Nicolson method based on the shifted Gr"{u}nwald formula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solution for its order of convergence.

A second-order accurate numerical approximation for two-sided fractional boundary value advection-diffusion problem

Authors [Persian]

Elyas Shivanian; Hamid Reza Khodabandehlo

^{}

Abstract [Persian]

Fractional order partial differential equations are generalization of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. An approach based on the classical Crank-Nicolson method combined with spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Stability, consistency, and convergence of the method are examined. It is shown that the fractional Crank-Nicolson method based on the shifted Gr"{u}nwald formula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solution for its order of convergence.

Fractional order partial differential equations are generalization of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. An approach based on the classical Crank-Nicolson method combined with spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Stability, consistency, and convergence of the method are examined. It is shown that the fractional Crank-Nicolson method based on the shifted Gr"{u}nwald formula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solution for its order of convergence.