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《Journal of North University of China(Natural Science Edition)》 2014-01
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An Implicit Difference Approximation for Variable Coefficients Space Fractional Convection-Diffusion Equation

MA Liang-liang;TIAN Fu-peng;College of Mathematics and Computer,Panzhihua University;Institute of Modern Educational Technology,Northwest University for Nationalities;  
On the basis of the classical convection-diffusion equation,an implicit difference scheme for variable coefficients space fractional convection-diffusion equation was investigated.A computationally effective implicit difference approximation was obtained by using the modified formula of Grünwald joined with two first order approximations of the first order time derivative and first space derivative to discrete the fractional derivatives.Then,using the characteristic of the fractional discrete coefficients and Lax equivalent theorem,the fractional implicit difference approximation proved is unconditional stable,and the convergence of the approximation is also proved.Finally,illustrative example is included to demonstrate the validity and applicability of the difference scheme.
【Fund】: 国家自然科学基金资助项目(60673192)
【CateGory Index】: O241.82
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