Two classes of efficient and robust schemes are proposed for the general multi-symplectic
Hamiltonian systems using the invariant energy quadratization (IEQ) approach. The …

In this paper, we investigate the (2+ 1)-dimensional coupled nonlinear Schrödinger
equations with perturbed dispersion and nonlinearity, which govern the transverse effects in …

Since the emergence of numerical methods in mathematical modeling, fundamental
properties such as convergence, efficiency, computational accuracy, and stability have been …

Temporal second-and high-order efficient one-step schemes are proposed for the damped
nonlinear Schrödinger equation in high dimensions by combining the integrating factor …

In this paper we propose several efficient conservative prediction-correction methods for
studying the Schrödinger equation in the semiclassical regimes with small parameter ε. In …

Efficient, mass-and energy-preserving schemes are developed for the multi-dimensional
coupled nonlinear Schrödinger–Boussinesq system. In the scheme, the solution u n+ 1 is …

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 article, stochastic conformal schemes of the damped stochastic Klein-Gordon
equation with additive noise are studied. It is shown that this equation possesses the …

General and refined spatiotemporal similariton solutions are presented by introducing
arbitrary real temporal and spatial modulation functions that construct flexible 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 …