Discretized fractional calculus
SIAM Journal on Mathematical Analysis
A numerical method for a partial integro-differential equation
SIAM Journal on Numerical Analysis
A difference scheme for a nonlinear partial integrodifferential equation
SIAM Journal on Numerical Analysis
Applied Mathematics and Computation
Numerical solution of partial differential equations
Numerical solution of partial differential equations
Mathematics of Computation
Discretization with variable time steps of an evolution equation with a positive-type memory term
Journal of Computational and Applied Mathematics
Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
Implicit finite difference approximation for time fractional diffusion equations
Computers & Mathematics with Applications
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
Journal of Computational and Applied Mathematics
Numerical simulations of 2D fractional subdiffusion problems
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
Numerical solution of two-sided space-fractional wave equation using finite difference method
Journal of Computational and Applied Mathematics
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
A tau approach for solution of the space fractional diffusion equation
Computers & Mathematics with Applications
Numerical approximations for fractional diffusion equations via splines
Computers & Mathematics with Applications
Effects of a fractional friction with power-law memory kernel on string vibrations
Computers & Mathematics with Applications
The BEM for numerical solution of partial fractional differential equations
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
Applied Numerical Mathematics
Numerical treatment for solving the perturbed fractional PDEs using hybrid techniques
Journal of Computational Physics
Computers & Mathematics with Applications
Orthogonal spline collocation methods for the subdiffusion equation
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Journal of Computational Physics
Two finite difference schemes for time fractional diffusion-wave equation
Numerical Algorithms
Hi-index | 31.50 |
A class of finite difference methods for solving fractional diffusion equations is considered. These methods are an extension of the weighted average methods for ordinary (non-fractional) diffusion equations. Their accuracy is of order (Δ x)2 and Δt, except for the fractional version of the Crank-Nicholson method, where the accuracy with respect to the timestep is of order (Δt)2 if a second-order approximation to the fractional time-derivative is used. Their stability is analyzed by means of a recently proposed procedure akin to the standard von Neumann stability analysis. A simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order of the fractional derivative, is found and checked numerically. Some examples are provided in which the new methods' numerical solutions are obtained and compared against exact solutions.