The paper provides an introduction and survey of conservative discretization methods for
Hamiltonian partial differential equations. The emphasis is on variational, symplectic and …

Numerical integration of differential equations, as an essential tool for investigating the
qualitative behaviour of the physical universe, is a very active research area since large …

In this paper we discuss energy conservation issues related to the numerical solution of the
semilinear wave equation. As is well known, this problem can be cast as a Hamiltonian …

In this paper, we further develop recent results in the numerical solution of Hamiltonian
partial differential equations (PDEs)(Brugnano et al., 2015), by means of energy-conserving …

In this review we collect some recent achievements in the accurate and efficient solution of
the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian …

In this paper we propose and investigate a general approach to constructing local energy-
preserving algorithms which can be of arbitrarily high order in time for solving Hamiltonian …

In this paper we explore the local and global properties of multisymplectic discretizations
based on finite differences and Fourier spectral approximations. Multisymplectic (MS) …

Geometric discretizations that preserve certain Hamiltonian structures at the discrete level
has been proven to enhance the accuracy of numerical schemes. In particular, numerous …

We consider for the integration of coupled nonlinear Schrödinger equations with periodic
plane wave solutions a splitting method from the class of symplectic integrators and the multi …

In this paper, we derive a series of local structure-preserving algorithms for the “good”
Boussinesq equation, including multisymplectic geometric structure-preserving algorithms …