Linearly implicit local and global energy-preserving methods for Hamiltonian PDEs

Abstract

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.