In this paper, an efficient method seeking the numerical solution of a time-fractional
convection equation whose solution is not smooth at the starting time is presented. The …

For the nonlinear conservative system, how to design an efficient scheme to preserve as
manyinvariants as possible is a challenging task. The aim of this paper is to construct the …

We construct three efficient and accurate numerical methods for solving the Klein–Gordon–
Schrödinger (KGS) equations with/without damping terms. The first one is based on the …

Mass and energy conservative numerical methods are proposed for a general system of N
strongly coupled nonlinear Schrödinger equations (N-CNLS). Motivated by the structure …

In this study, we construct three efficient and conservative high-order accurate finite
difference schemes for solving the Klein-Gordon-Schrödinger equations with homogeneous …

In this manuscript, we consider an efficient dissipation-preserving finite element method for a
class of two-dimensional nonlinear fractional wave equations on irregular convex domains …

A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate
conservation laws for various physical systems. The distributed parameter port-Hamiltonian …

In this paper, a novel auxiliary variable approach is firstly introduced to reformulate the
fractional nonlinear Schrödinger equation with wave operator in an equivalent system …

Using a unified framework, the formulation of a super-convergent discontinuous Galerkin
(SDG) method and a hybridized discontinuous Galerkin (HDG) version, both applied to a …

This paper is concerned with unconditionally optimal error estimates of linearized leap-frog
Galerkin finite element methods (FEMs) to numerically solve the d-dimensional (d= 2, 3)(d …