Sharp error estimate of the nonuniform L1 formula for linear reaction-subdiffusion equations
Stability and convergence of the L1 formula on nonuniform time grids are studied for solving
linear reaction-subdiffusion equations with the Caputo derivative. A discrete fractional …
linear reaction-subdiffusion equations with the Caputo derivative. A discrete fractional …
A discrete Gronwall inequality with applications to numerical schemes for subdiffusion problems
We consider a class of numerical approximations to the Caputo fractional derivative. Our
assumptions permit the use of nonuniform time steps, such as is appropriate for accurately …
assumptions permit the use of nonuniform time steps, such as is appropriate for accurately …
Unconditionally Convergent -Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
In this paper, a linearized L1-Galerkin finite element method is proposed to solve the
multidimensional nonlinear time-fractional Schrödinger equation. In terms of a temporal …
multidimensional nonlinear time-fractional Schrödinger equation. In terms of a temporal …
Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations: a second-order scheme
The fractional derivatives include nonlocal information and thus their calculation requires
huge storage and computational cost for long time simulations. We present an efficient and …
huge storage and computational cost for long time simulations. We present an efficient 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 …
[图书][B] Numerical treatment and analysis of time-fractional evolution equations
The purpose of this book is to present a self-contained and up-to-date survey of numerical
treatment for the so-called time-fractional diffusion model and their mathematical analysis …
treatment for the so-called time-fractional diffusion model and their mathematical analysis …
[PDF][PDF] A novel numerical approach to time-fractional parabolic equations with nonsmooth solutions
This paper is concerned with numerical solutions of time-fractional parabolic equations. Due
to the Caputo time derivative being involved, the solutions of equations are usually singular …
to the Caputo time derivative being involved, the solutions of equations are usually singular …
Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations
Recently there has been a growing interest in designing efficient numerical methods for the
solution of fractional differential equations. The solutions of such equations in general …
solution of fractional differential equations. The solutions of such equations in general …
Exponential convolution quadrature for nonlinear subdiffusion equations with nonsmooth initial data
An exponential type of convolution quadrature is proposed as a time-stepping method for
the nonlinear subdiffusion equation with bounded measurable initial data. The method …
the nonlinear subdiffusion equation with bounded measurable initial data. The method …