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
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
Advances in Engineering Software
Journal of Computational and Applied Mathematics
Anomalous diffusion modeling by fractal and fractional derivatives
Computers & Mathematics with Applications
Fractional diffusion equations by the Kansa method
Computers & Mathematics with Applications
A direct O(Nlog2N) finite difference method for fractional 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
Computers & Mathematics with Applications
A characteristic difference method for the transient fractional convection-diffusion equations
Applied Numerical Mathematics
Application of Legendre wavelets for solving fractional differential equations
Computers & Mathematics with Applications
Multigrid method for fractional diffusion equations
Journal of Computational Physics
Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
Journal of Computational Physics
Journal of Computational Physics
Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models
Computational Economics
Error Estimates of Crank-Nicolson-Type Difference Schemes for the Subdiffusion Equation
SIAM Journal on Numerical Analysis
Numerical methods and analysis for a class of fractional advection-dispersion models
Computers & Mathematics with Applications
Regularization methods for unknown source in space fractional diffusion equation
Mathematics and Computers in Simulation
A radial basis functions method for fractional diffusion equations
Journal of Computational Physics
A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations
Journal of Computational Physics
Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods
Numerical Algorithms
Applied Numerical Mathematics
A circulant preconditioner for fractional diffusion equations
Journal of Computational Physics
Original article: An optimal regularization method for space-fractional backward diffusion problem
Mathematics and Computers in Simulation
Numerical treatment for solving the perturbed fractional PDEs using hybrid techniques
Journal of Computational Physics
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
Fast solution methods for space-fractional diffusion equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Preconditioned iterative methods for fractional diffusion equation
Journal of Computational Physics
Numerical and analytical solutions of new generalized fractional diffusion equation
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Journal of Computational Physics
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Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. We examine the case when a left-handed or a right-handed fractional spatial derivative may be present in the partial differential equation. Stability, consistency, and (therefore) convergence of the methods are discussed. The stability (and convergence) results in the fractional PDE unify the corresponding results for the classical parabolic and hyperbolic cases into a single condition. A numerical example using a finite difference method for a two-sided fractional PDE is also presented and compared with the exact analytical solution.