We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multi-symplectic PDEs with cubic invariants. The methods are tested on the one-dimensional Korteweg–de Vries equation and the two-dimensional Zakharov–Kuznetsov equation; the numerical simulations confirm the conservative properties of the methods, and demonstrate their good stability properties and superior running speed when compared to fully implicit schemes
Abstract. Multi-symplectic methods have recently been proposed as a generalization of symplectic ODE...
Conservation laws are among the most fundamental geometric properties of a given partial differentia...
In this paper, we further develop recent results in the numerical solution of Hamiltonian partial di...
Released as supplementary material to the article "Linearly implicit local and global energy-preserv...
Kahan’s method and a two-step generalization of the discrete gradient method are both linearly impli...
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with ...
Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (R...
There are several well-established approaches to constructing finite difference schemes that preserv...
Recent results on the local and global properties of multisymplectic discretizations of Hamiltonian ...
Although Runge-Kutta and partitioned Runge-Kutta methods are known to formally satisfy discrete mult...
In this paper, we study the preservation of quadratic conservation laws of Runge-Kutta methods and p...
Recent results on the local and global properties of multisymplectic discretizations of Hamiltonian ...
textabstractMultisymplectic methods have recently been proposed as a generalization of symplectic OD...
A useful method for understanding discretization error in the numerical solution of ODEs is to compa...
This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE...
Abstract. Multi-symplectic methods have recently been proposed as a generalization of symplectic ODE...
Conservation laws are among the most fundamental geometric properties of a given partial differentia...
In this paper, we further develop recent results in the numerical solution of Hamiltonian partial di...
Released as supplementary material to the article "Linearly implicit local and global energy-preserv...
Kahan’s method and a two-step generalization of the discrete gradient method are both linearly impli...
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with ...
Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (R...
There are several well-established approaches to constructing finite difference schemes that preserv...
Recent results on the local and global properties of multisymplectic discretizations of Hamiltonian ...
Although Runge-Kutta and partitioned Runge-Kutta methods are known to formally satisfy discrete mult...
In this paper, we study the preservation of quadratic conservation laws of Runge-Kutta methods and p...
Recent results on the local and global properties of multisymplectic discretizations of Hamiltonian ...
textabstractMultisymplectic methods have recently been proposed as a generalization of symplectic OD...
A useful method for understanding discretization error in the numerical solution of ODEs is to compa...
This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE...
Abstract. Multi-symplectic methods have recently been proposed as a generalization of symplectic ODE...
Conservation laws are among the most fundamental geometric properties of a given partial differentia...
In this paper, we further develop recent results in the numerical solution of Hamiltonian partial di...