Numerical solution of the space fractional Fokker-Planck equation
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Numerical approaches to fractional calculus and fractional ordinary differential equation
Journal of Computational Physics
Computers & Mathematics with Applications
Improved matrix transform method for the Riesz space fractional reaction dispersion equation
Journal of Computational and Applied Mathematics
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In this paper, we consider the numerical solution of the Riesz space fractional diffusion equation and advection-dispersion equation. First, a system of ordinary differential equations is obtained from the above equations with respect to the space variable by using the improved matrix transform method. Furthermore, we use the (2,2) Pade approximation to compute the exponential matrix in the analytic solution of the ordinary differential equation, and get two difference schemes. Second, using the matrix analysis method, we prove that the two difference schemes are unconditionally stable. Finally, some numerical results are given, which demonstrate the effectiveness of the two difference schemes.