A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations
In this review article we discuss different techniques to solve numerically the time-dependent
Schrödinger equation on unbounded domains. We present in detail the most recent …
Schrödinger equation on unbounded domains. We present in detail the most recent …
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 …
The AAA algorithm for rational approximation
We introduce a new algorithm for approximation by rational functions on a real or complex
set of points, implementable in 40 lines of MATLAB and requiring no user input parameters …
set of points, implementable in 40 lines of MATLAB and requiring no user input parameters …
[КНИГА][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 …
Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations
The computational work and storage of numerically solving the time fractional PDEs are
generally huge for the traditional direct methods since they require total memory and work …
generally huge for the traditional direct methods since they require total memory and work …
Radiation boundary conditions for the numerical simulation of waves
T Hagstrom - Acta numerica, 1999 - cambridge.org
We consider the efficient evaluation of accurate radiation boundary conditions for time
domain simulations of wave propagation on unbounded spatial domains. This issue has …
domain simulations of wave propagation on unbounded spatial domains. This issue has …
On approximation of functions by exponential sums
We introduce a new approach, and associated algorithms, for the efficient approximation of
functions and sequences by short linear combinations of exponential functions with complex …
functions and sequences by short linear combinations of exponential functions with complex …
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 …
[КНИГА][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 …
High-order non-reflecting boundary scheme for time-dependent waves
A new non-reflecting boundary scheme is proposed for time-dependent wave problems in
unbounded domains. The linear time-dependent wave equation, with or without a dispersive …
unbounded domains. The linear time-dependent wave equation, with or without a dispersive …