A Stable Penalty Method for the Compressible Navier--Stokes Equations: I. Open Boundary Conditions
SIAM Journal on Scientific Computing
Spectral methods on arbitrary grids
Journal of Computational Physics
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
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
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
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
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Functional Fractional Calculus for System Identification and Controls
Functional Fractional Calculus for System Identification and Controls
Finite Element Method for the Space and Time Fractional Fokker-Planck Equation
SIAM Journal on Numerical Analysis
A Space-Time Spectral Method for the Time Fractional Diffusion Equation
SIAM Journal on Numerical Analysis
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
Numerical approximations for fractional diffusion equations via splines
Computers & Mathematics with Applications
Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
Journal of Computational Physics
Journal of Computational Physics
Error Estimates of Crank-Nicolson-Type Difference Schemes for the Subdiffusion Equation
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.