DeepAI AI Chat
Log In Sign Up

Energy-preserving multi-symplectic Runge-Kutta methods for Hamiltonian wave equations

by   Chuchu Chen, et al.
Chinese Academy of Science

It is well-known that a numerical method which is at the same time geometric structure-preserving and physical property-preserving cannot exist in general for Hamiltonian partial differential equations. In this paper, we present a novel class of parametric multi-symplectic Runge-Kutta methods for Hamiltonian wave equations, which can also conserve energy simultaneously in a weaker sense with a suitable parameter. The existence of such a parameter, which enforces the energy-preserving property, is proved under certain assumptions on the fixed step sizes and the fixed initial condition. We compare the proposed method with the classical multi-symplectic Runge-Kutta method in numerical experiments, which shows the remarkable energy-preserving property of the proposed method and illustrate the validity of theoretical results.


page 1

page 2

page 3

page 4


Three kinds of novel multi-symplectic methods for stochastic Hamiltonian partial differential equations

Stochastic Hamiltonian partial differential equations, which possess the...

Numerical integration of ODEs while preserving all polynomial first integrals

We present a novel method for solving ordinary differential equations (O...

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

We present a numerical approach for approximating unknown Hamiltonian sy...

Effective Numerical Simulations of Synchronous Generator System

Synchronous generator system is a complicated dynamical system for energ...

Bridging the gap: symplecticity and low regularity on the example of the KdV equation

Recent years have seen an increasing amount of research devoted to the d...

Canonical and Noncanonical Hamiltonian Operator Inference

A method for the nonintrusive and structure-preserving model reduction o...