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 …
[BOOK][B] Numerical methods for fractional calculus
This book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …
[BOOK][B] Theory and numerical approximations of fractional integrals and derivatives
C Li, M Cai - 2019 - SIAM
Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …
means integration and differentiation of any positive real order or even complex order. It has …
Numerical approaches to fractional integrals and derivatives: a review
M Cai, C Li - Mathematics, 2020 - mdpi.com
Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …
Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
In this paper, compact finite difference schemes for the modified anomalous fractional sub-
diffusion equation and fractional diffusion-wave equation are studied. Schemes proposed …
diffusion equation and fractional diffusion-wave equation are studied. Schemes proposed …
A fourth-order compact ADI scheme for two-dimensional nonlinear space fractional Schrodinger equation
In this paper, a novel compact operator is derived for the approximation of the Riesz
derivative with order α∈(1,2. The compact operator is proved with fourth-order accuracy …
derivative with order α∈(1,2. The compact operator is proved with fourth-order accuracy …
Efficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biology
In this work, the solution of Riesz space fractional partial differential equations of parabolic
type is considered. Since fractional-in-space operators have been applied to model …
type is considered. Since fractional-in-space operators have been applied to model …
An improved collocation method for multi-dimensional space–time variable-order fractional Schrödinger equations
Current discretizations of variable-order fractional (V-OF) differential equations lead to
numerical solutions of low order of accuracy. This paper explores a high order numerical …
numerical solutions of low order of accuracy. This paper explores a high order numerical …
Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations
A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP)
in the sense that the time-dependent solution preserves for any time a uniform pointwise …
in the sense that the time-dependent solution preserves for any time a uniform pointwise …
Numerical analysis of fully discretized Crank–Nicolson scheme for fractional-in-space Allen–Cahn equations
We consider numerical methods for solving the fractional-in-space Allen–Cahn equation
which contains small perturbation parameters and strong nonlinearity. A standard fully …
which contains small perturbation parameters and strong nonlinearity. A standard fully …