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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…
Second order finite difference approximations for the two-dimensional time-space Caputo-Riesz fractional diffusion equation
Minghua Chen, Weihua Deng, Yujiang Wu
In this paper, we discuss the time-space Caputo-Riesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation a…
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…
Jacobi-Predictor-Corrector Approach for the Fractional Ordinary Differential Equations
Lijing Zhao, Weihua Deng
We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynom…
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…