Linearly Implicit Local And Global Energy-Preserving Methods For Pdes With A Cubic Hamiltonian

We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multisymplectic partial differential equations 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.