This paper presents two kinds of strategies to construct structure-preserving algorithms with
homogeneous Neumann boundary conditions for the sine-Gordon equation, while most …

In this paper, we present a quadratic auxiliary variable (QAV) technique to develop a novel
class of arbitrarily high-order energy-preserving algorithms for the Camassa-Holm equation …

This paper focuses on the construction and analysis of the energy-conserving numerical
schemes for the generalized nonlinear space fractional Schrödinger equations with wave …

The main contribution of this article is to introduce new compact fourth-order, standard fourth-
order, and standard second-order finite difference schemes for solving the Kawahara …

In this paper, we present a linearly implicit energy-preserving scheme for the Camassa–
Holm equation by using the multiple scalar auxiliary variables approach, which is first …

Continental magmatic arcs are characterized by the accretion of voluminous mantle-derived
magmatic rocks and the growth of juvenile crust. However, significant volumes of meta …

In this paper, we consider leap‐frog finite element methods with EQ 1 rot EQ _1^ rot element
for the nonlinear Schrödinger equation with wave operator. We propose that both the …

A general framework for constructing energy dissipative or conservative Galerkin schemes
for time-dependent partial differential equations (PDEs) is presented. The framework …

This paper gives several structure-preserving schemes for the Degasperis-Procesi equation
which has bi-Hamiltonian structures consisted of both complex and non-local Hamiltonian …

In this paper, the local discontinuous Galerkin method is developed to solve the two-
dimensional Camassa–Holm equation in rectangular meshes. The idea of LDG methods is …