Global and exploding solutions for nonlocal quadratic evolution problems
SIAM Journal on Applied Mathematics
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
Short memory principle and a predictor-corrector approach for fractional differential equations
Journal of Computational and Applied Mathematics
Numerical Approximation of a Time Dependent, Nonlinear, Space-Fractional Diffusion Equation
SIAM Journal on Numerical Analysis
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical algorithm based on Adomian decomposition for fractional differential equations
Computers & Mathematics with Applications
On the fractional Adams method
Computers & Mathematics with Applications
SIAM Journal on Numerical Analysis
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
A note on the finite element method for the space-fractional advection diffusion equation
Computers & Mathematics with Applications
Numerical approaches to fractional calculus and fractional ordinary differential equation
Journal of Computational Physics
New numerical methods for the Riesz space fractional partial differential equations
Computers & Mathematics with Applications
Finite Elements in Analysis and Design
A numerical approach to the generalized nonlinear fractional Fokker-Planck equation
Computers & Mathematics with Applications
A second order explicit finite difference method for the fractional advection diffusion equation
Computers & Mathematics with Applications
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Boundary particle method for Laplace transformed time fractional diffusion equations
Journal of Computational Physics
Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods
Numerical Algorithms
Mixed spline function method for reaction-subdiffusion equations
Journal of Computational Physics
Journal of Scientific Computing
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Time-fractional heat equations and negative absolute temperatures
Computers & Mathematics with Applications
Two finite difference schemes for time fractional diffusion-wave equation
Numerical Algorithms
Fully discrete local discontinuous Galerkin method for solving the fractional telegraph equation
Calcolo: a quarterly on numerical analysis and theory of computation
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In this paper, we study the time-space fractional order (fractional for simplicity) nonlinear subdiffusion and superdiffusion equations, which can relate the matter flux vector to concentration gradient in the general sense, describing, for example, the phenomena of anomalous diffusion, fractional Brownian motion, and so on. The semi-discrete and fully discrete numerical approximations are both analyzed, where the Galerkin finite element method for the space Riemann-Liouville fractional derivative with order 1+@b@?[1,2] and the finite difference scheme for the time Caputo derivative with order @a@?(0,1) (for subdiffusion) and (1,2) (for superdiffusion) are analyzed, respectively. Results on the existence and uniqueness of the weak solutions, the numerical stability, and the error estimates are presented. Numerical examples are included to confirm the theoretical analysis. During our simulations, an interesting diffusion phenomenon of particles is observed, that is, on average, the diffusion velocity for 0