Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
Wave field simulation for heterogeneous porous media with singular memory drag force
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Signal Processing - Fractional calculus applications in signals and systems
Short memory principle and a predictor-corrector approach for fractional differential equations
Journal of Computational and Applied Mathematics
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
Numerical treatment of fractional heat equations
Applied Numerical Mathematics
Computers & Mathematics with Applications
Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives
Journal of Computational and Applied Mathematics
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Fractional differential equations in electrochemistry
Advances in Engineering Software
A Space-Time Spectral Method for the Time Fractional Diffusion Equation
SIAM Journal on Numerical Analysis
Least squares finite-element solution of a fractional order two-point boundary value problem
Computers & Mathematics with Applications
Pitfalls in fast numerical solvers for fractional differential equations
Journal of Computational and Applied Mathematics
A note on the finite element method for the space-fractional advection diffusion equation
Computers & Mathematics with Applications
Computers & Mathematics with Applications
A Fast Time Stepping Method for Evaluating Fractional Integrals
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
Fractional derivatives provide a general approach for modeling transport phenomena occurring in diverse fields. This article describes a Least Squares Spectral Method for solving advection-dispersion equations using Caputo or Riemann-Liouville fractional derivatives. A Gauss-Lobatto-Jacobi quadrature is implemented to approximate the singularities in the integrands arising from the fractional derivative definition. Exponential convergence rate of the operator is verified when increasing the order of the approximation. Solutions are calculated for fractional-time and fractional-space differential equations. Comparisons with finite difference schemes are included. A significant reduction in storage space is achieved by lowering the resolution requirements in the time coordinate.