Solving differential equations of fractional (ie, non-integer) order in an accurate, reliable and
efficient way is much more difficult than in the standard integer-order case; moreover, the …

A new fourth-order difference approximation is derived for the space fractional derivatives by
using the weighted average of the shifted Grünwald formulae combining the compact …

This paper provides a new numerical strategy for solving fractional-in-space reaction-
diffusion equations on bounded domains under homogeneous Dirichlet boundary …

The time-fractional Schrödinger equation is a fundamental topic in physics and its numerical
solution is still an open problem. Here we start from the possibility to express its solution by …

In this paper, we consider the time-dependent Schrödinger equation: i∂ ψ (x, t)∂ t= 1 2 (−
Δ) α 2 ψ (x, t)+ V (x) ψ (x, t), x∈ R, t> 0 with the Riesz space-fractional derivative of order 0< …

A fourth-order implicit-explicit time-discretization scheme based on the exponential time
differencing approach with a fourth-order compact scheme in space is proposed for space …

In this paper, by combining of fractional centered difference approach with alternating
direction implicit method, we introduce a mixed difference method for solving two …

This paper presents a deep analysis of a time-dependent Schrödinger equation with
fractional time derivative. After the discretization of the spatial operator the equation is …

An innovative block structured with sparse blocks multi iterative preconditioner for linear
multistep formulas used in boundary value form is proposed here to accelerate GMRES …

The efficient numerical solution of the large linear systems of fractional differential equations
is considered here. The key tool used is the short–memory principle. The latter ensures the …