We propose a nodal discontinuous Galerkin method for solving the nonlinear Riesz space
fractional Schrödinger equation and the strongly coupled nonlinear Riesz space fractional …

Whether high order temporal integrators can preserve the maximum principle of Allen-Cahn
equation has been an open problem in recent years. This work provides a positive answer …

A novel class of high-order linearly implicit energy-preserving integrating factor Runge–
Kutta methods are proposed for the nonlinear Schrödinger equation. Based on the idea of …

In this work, the error splitting technique combined with cut-off function method is designed
to derive unconditionally optimal error estimates for a fully implicit conservative numerical …

In this paper, we reformulate the coupled nonlinear Schrödinger (CNLS) equation by using
the scalar auxiliary variable (SAV) approach and solve the resulting system by using Crank …

A family of arbitrarily high-order fully discrete space-time finite element methods are
proposed for the nonlinear Schrödinger equation based on the scalar auxiliary variable …

We present, in a unified framework, conforming and nonconforming virtual element methods
for nonlinear Schrödinger equation. The constructed schemes conserve not only the mass …

We present a systematic two-step approach to derive temporal up to the eighth-order,
unconditionally maximum-principle-preserving schemes for a semilinear parabolic sine …

In this paper, a family of arbitrarily high-order structure-preserving exponential Runge–Kutta
methods are developed for the nonlinear Schrödinger equation by combining the scalar …

We carry out efforts to reproduce computational results for seven published articles and
identify barriers to computational reproducibility. We then derive three principles to guide the …