Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
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
SIAM Journal on Numerical Analysis
Finite difference approximations for two-sided space-fractional partial differential equations
Applied Numerical Mathematics
Finite difference methods for two-dimensional fractional dispersion equation
Journal of Computational Physics
A second-order accurate numerical approximation for the fractional diffusion equation
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Numerical solutions for fractional reaction-diffusion equations
Computers & Mathematics with Applications
Numerical treatment of fractional heat equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Finite difference approximations for a fractional advection diffusion problem
Journal of Computational Physics
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
Computing the Local Continuity Order of Optical Flow Using Fractional Variational Method
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Journal of Computational and Applied Mathematics
Numerical solution of two-sided space-fractional wave equation using finite difference method
Journal of Computational and Applied Mathematics
Multiscale analysis of volumetric motion field using general order prior
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
A characteristic difference method for the transient fractional convection-diffusion equations
Applied Numerical Mathematics
The Grünwald-Letnikov method for fractional differential equations
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Application of Legendre wavelets for solving fractional differential equations
Computers & Mathematics with Applications
Compact alternating direction implicit method for two-dimensional time fractional diffusion equation
Journal of Computational Physics
Variational iteration method for the time-fractional Fornberg-Whitham equation
Computers & Mathematics with Applications
Error Estimates of Crank-Nicolson-Type Difference Schemes for the Subdiffusion Equation
SIAM Journal on Numerical Analysis
Boundary particle method for Laplace transformed time fractional diffusion equations
Journal of Computational Physics
A radial basis functions method for fractional diffusion equations
Journal of Computational Physics
Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods
Numerical Algorithms
Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion Equations
Journal of Scientific Computing
Efficient computational algorithms for solving one class of fractional boundary value problems
Computational Mathematics and Mathematical Physics
A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation
Computers & Mathematics with Applications
Convergence analysis of moving finite element methods for space fractional differential equations
Journal of Computational and Applied Mathematics
Stable multi-domain spectral penalty methods for fractional partial differential equations
Journal of Computational Physics
Computers & Mathematics with Applications
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Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. In this paper, we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation. This numerical method combines the alternating directions implicit (ADI) approach with a Crank-Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. The stability and the consistency of the method are established. Numerical solutions for an example super-diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method.