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 work, a novel class of high-order energy-preserving algorithms are developed for
simulating the coupled Klein-Gordon-Schrödinger equations. We introduce a Lagrange …

In this paper, we propose the conservative linearized Galerkin finite element methods
(FEMs) for the nonlinear Klein-Gordon-Schrödinger equation (KGSE) with homogeneous …

The classic second-order averaged vector field (AVF) method can exactly preserve the
energy for Hamiltonian systems. However, the AVF method inevitably leads to fully-implicit …

We present a class of arbitrarily high-order conservative schemes for the Klein–Gordon
Schrödinger equations. These schemes combine the symplectic Runge–Kutta method with …

For diagonal sparse matrices that have many long zero sections or scatter points or diagonal
deviations from the main diagonal, a great number of zeros need be filled to maintain the …

The focus of this paper is on the optimal error bounds of a Fourier pseudo-spectral
conservative scheme for solving the 2-dimensional nonlinear Klein–Gordon–Schrödinger …

In this paper, we design two classes of high-accuracy conservative numerical algorithms for
the nonlinear Klein-Gordon-Schrödinger system in two dimensions. By introducing the …

In this paper, we propose an efficient numerical scheme for the space-fractional Klein–
Gordon–Schrödinger (SFKGS) equations. Motivated by the “Invariant Energy …

Recently, the long time numerical simulation of PDEs with weak nonlinearity (or small
potentials) becomes an interesting topic. In this paper, for the Klein–Gordon–Schrödinger …