Finite difference methods for two-dimensional fractional dispersion equation
Journal of Computational Physics
Weighted average finite difference methods for fractional diffusion equations
Journal of Computational Physics
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
Convergence of the Grünwald-Letnikov scheme for time-fractional diffusion
Journal of Computational and Applied Mathematics
A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics
Implicit finite difference approximation for time fractional diffusion equations
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Finite difference approximations for a fractional advection diffusion problem
Journal of Computational Physics
Explicit methods for fractional differential equations and their stability properties
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
Explicit and implicit finite difference schemes for fractional Cattaneo equation
Journal of Computational Physics
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation
Numerical Algorithms
Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
SIAM Journal on Scientific Computing
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Numerical analysis and physical simulations for the time fractional radial diffusion equation
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Numerical approximations for fractional diffusion equations via splines
Computers & Mathematics with Applications
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Compact alternating direction implicit method for two-dimensional time fractional diffusion equation
Journal of Computational Physics
Error Estimates of Crank-Nicolson-Type Difference Schemes for the Subdiffusion Equation
SIAM Journal on Numerical Analysis
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods
Numerical Algorithms
Mixed spline function method for reaction-subdiffusion equations
Journal of Computational Physics
Stable multi-domain spectral penalty methods for fractional partial differential equations
Journal of Computational Physics
Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
Journal of Scientific Computing
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A numerical method for solving the fractional diffusion equation, which could also be easily extended to other fractional partial differential equations, is considered. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grünwald--Letnikov discretization of the Riemann--Liouville derivative to obtain an explicit FTCS scheme for solving the fractional diffusion equation. The stability analysis of this scheme is carried out by means of a powerful and simple new procedure close to the well-known von Neumann method for nonfractional partial differential equations. The analytical stability bounds are in excellent agreement with numerical test. A comparison between exact analytical solutions and numerical predictions is made.