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math.NA2012★ 66 cited
Polynomial Spectral collocation Method for Space Fractional Advection-Diffusion Equation
WenYi Tian, Weihua Deng, Yujiang Wu
This paper discusses the spectral collocation method for numerically solving nonlocal problems: one dimensional space fractional advection-diffusion equation; and two dimensional l…
math.NA2012★ 156 cited
Compact Finite Difference Approximations for Space Fractional Diffusion Equations
Han Zhou, WenYi Tian, Weihua Deng
Based on the weighted and shifted Grünwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then t…
math.NA2012★ 659 cited
A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations
WenYi Tian, Han Zhou, Weihua Deng
A class of second order approximations, called the weighted and shifted Grünwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effecti…