The ubiquitous Kronecker product
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
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
Numerical inversion of 2-D Laplace transforms applied to fractional diffusion equations
Applied Numerical Mathematics
Numerical study of interacting particles approximation for integro-differential equations
Journal of Computational Physics
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
Wave field simulation for heterogeneous porous media with singular memory drag force
Journal of Computational Physics
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
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
Journal of Computational Physics
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
Numerical treatment of fractional heat equations
Applied Numerical Mathematics
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
Fractional order control: a tutorial
ACC'09 Proceedings of the 2009 conference on American Control Conference
ETFA'09 Proceedings of the 14th IEEE international conference on Emerging technologies & factory automation
Block pulse-based techniques for modelling and synthesis of non-integer systems
International Journal of Systems Science
A fractional state space realization method with block pulse basis
Signal Processing
On nonlinear fractional Klein-Gordon equation
Signal Processing
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
Modeling and numerical analysis of fractional-order Bloch equations
Computers & Mathematics with Applications
Fractional Bloch equation with delay
Computers & Mathematics with Applications
Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
SIAM Journal on Scientific Computing
Numerical approaches to fractional calculus and fractional ordinary differential equation
Journal of Computational Physics
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
The BEM for numerical solution of partial fractional differential equations
Computers & Mathematics with Applications
Compact alternating direction implicit method for two-dimensional time fractional diffusion equation
Journal of Computational Physics
Numerical methods and analysis for a class of fractional advection-dispersion models
Computers & Mathematics with Applications
Least-Squares Spectral Method for the solution of a fractional advection-dispersion equation
Journal of Computational Physics
A radial basis functions method for fractional diffusion equations
Journal of Computational Physics
Computers & Mathematics with Applications
Hi-index | 31.48 |
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny's matrix approach [I. Podlubny, Matrix approach to discrete fractional calculus, Fractional Calculus and Applied Analysis 3 (4) (2000) 359-386]. Four examples of numerical solution of fractional diffusion equation with various combinations of time-/space-fractional derivatives (integer/integer, fractional/integer, integer/fractional, and fractional/fractional) with respect to time and to the spatial variable are provided in order to illustrate how simple and general is the suggested approach. The fifth example illustrates that the method can be equally simply used for fractional differential equations with delays. A set of MATLAB routines for the implementation of the method as well as sample code used to solve the examples have been developed.