A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-
dimensional nonlinear Schrödinger equation. By establishing the equivalence between the …

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, a linearly-implicit Fourier pseudo-spectral method which preserves discrete
mass and energy is developed for the time-dependent 3D Gross–Pitaevskii equation with …

We propose a meshless conservative Galerkin method for solving Hamiltonian wave
equations. We first discretize the equation in space using radial basis functions in a Galerkin …

In this paper, we propose a general meshless structure-preserving Galerkin method for
solving dissipative PDEs on surfaces. By posing the PDE in the variational formulation and …

Many PDEs can be recast into the general multi-symplectic formulation possessing three
local conservation laws. We devote the present paper to some systematic methods, which …

Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-
order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that …

We give a systematic, linearly implicit, local energy-preserving method for the general multi-
symplectic Hamiltonian system with cubic invariants by combining Kahan's discretization in …

In this paper, we present a novel energy-preserving scheme for solving time-dependent
partial differential equations with periodic solutions on non-uniform grids. The proposed …

Since the pioneering works of Ampère, Faraday, and Maxwell in the early days,
electromagnetism has become a fascinating area of physics, engineering, and mathematics …