Related papers: Arbitrary high-order structure-preserving methods …
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxiliary variable (SAV) approach and the additive Runge-Kutta…
In this paper, a novel high-order, mass and energy-conserving scheme is proposed for the regularized logarithmic Schr\"{o}dinger equation(RLogSE). Based on the idea of the supplementary variable method (SVM), we firstly reformulate the…
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order temporal discretizations are proposed based on this new…
In this paper, we propose a first order energy stable linear semi-implicit method for solving the Allen-Cahn-Ohta-Kawasaki equation. By introducing a new nonlinear term in the Ohta-Kawasaki free energy functional, all the system forces in…
Conservation properties of iterative methods applied to implicit finite volume discretizations of nonlinear conservation laws are analyzed. It is shown that any consistent multistep or Runge-Kutta method is globally conservative. Further,…
The energy dissipation law and maximum bound principle are significant characteristics of the Allen-Chan equation. To preserve discrete counterpart of these properties, the linear part of the target system is usually discretized implicitly,…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
This paper aims to construct structure-preserving numerical schemes for multi-dimensional space fractional Klein-Gordon-Schr\"{o}dinger equation, which are based on the newly developed partitioned averaged vector field methods. First, we…
A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…
In this paper, we construct stochastic symplectic Runge--Kutta (SSRK) methods of high strong order for Hamiltonian systems with additive noise. By means of colored rooted tree theory, we combine conditions of mean-square order 1.5 and…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
In this paper, a novel sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell's equations. The new scheme preserves five discrete energy conservation laws, three momentum conservation laws,…
We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-discrete version of the proposed method is based on a technique…
Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Here, these concepts are extended to the realm of iterative methods by formally defining locally conservative and flux…
An error analysis of a splitting method applied to the Zakharov system is given. The numerical method is a Lie-Trotter splitting in time that is combined with a Fourier collocation in space to a fully discrete method. First-order…
Stochastic Klein--Gordon--Schr\"odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel…
Stochastic Klein--Gordon--Schr\"odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel…
An explicit numerical strategy that practically preserves invariants is derived for conservative systems by combining an explicit high-order Runge-Kutta (RK) scheme with a simple modification of the standard projection approach, which is…