Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview
Over the past few decades, there has been substantial interest in evolution equations that
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …
Numerical methods for fractional partial differential equations
In this review paper, we are mainly concerned with the finite difference methods, the
Galerkin finite element methods, and the spectral methods for fractional partial differential …
Galerkin finite element methods, and the spectral methods for fractional partial differential …
An analysis of the modified L1 scheme for time-fractional partial differential equations with nonsmooth data
Y Yan, M Khan, NJ Ford - SIAM Journal on Numerical Analysis, 2018 - SIAM
We introduce a modified L1 scheme for solving time fractional partial differential equations
and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and …
and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and …
Linearized Galerkin FEMs for nonlinear time fractional parabolic problems with non-smooth solutions in time direction
A Newton linearized Galerkin finite element method is proposed to solve nonlinear time
fractional parabolic problems with non-smooth solutions in time direction. Iterative processes …
fractional parabolic problems with non-smooth solutions in time direction. Iterative processes …
Semi-implicit Galerkin–Legendre spectral schemes for nonlinear time-space fractional diffusion–reaction equations with smooth and nonsmooth solutions
For the first time in literature, semi-implicit spectral approximations for nonlinear Caputo time-
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …
Nonuniform Alikhanov linearized Galerkin finite element methods for nonlinear time-fractional parabolic equations
The solutions of the nonlinear time fractional parabolic problems usually undergo dramatic
changes at the beginning. In order to overcome the initial singularity, the temporal …
changes at the beginning. In order to overcome the initial singularity, the temporal …
Singularity preserving spectral collocation method for nonlinear systems of fractional differential equations with the right-sided Caputo fractional derivative
The numerical treatment of fractional differential equations in an accurate way is more
difficult to tackle than the standard integer-order counterpart, and occasionally non …
difficult to tackle than the standard integer-order counterpart, and occasionally non …
High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers
W Chen, K Wu, T Xiong - Journal of Computational Physics, 2023 - Elsevier
In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free
finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for …
finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for …
A novel scheme to capture the initial dramatic evolutions of nonlinear subdiffusion equations
The solution of the nonlinear subdiffusion equation has the initial layer and its initial energy
may decay very fast. Therefore, it is important to investigate the evolution of the solution at …
may decay very fast. Therefore, it is important to investigate the evolution of the solution at …
Stability of two-step spline collocation methods for initial value problems for fractional differential equations
This paper analyzes the numerical stability of a class of two-step spline collocation methods
for initial value problems for fractional differential equations. The stability region is …
for initial value problems for fractional differential equations. The stability region is …