A novel semi-analytical multiple invariants-preserving integrator for conservative PDEs
Numerical Analysis
2025-08-19 v2 Numerical Analysis
Abstract
Many conservative partial differential equations such as the Korteweg-de Vries (KdV) equation, and the nonlinear Schr\"{o}dinger equations, the Klein-Gordon equation have more than one invariant functionals. In this paper, we propose the definition of the discrete variational derivative, based on which, a novel semi-analytical multiple invariants-preserving integrator for the conservative partial differential equations is constructed by projection technique. The proposed integrators are shown to have the same order of accuracy as the underlying integrators. For applications, some concrete mass-momentum-energy-preserving integrators are derived for the KdV equation.
Keywords
Cite
@article{arxiv.2504.01307,
title = {A novel semi-analytical multiple invariants-preserving integrator for conservative PDEs},
author = {Wei Shi and Bin Wang and Kai Liu},
journal= {arXiv preprint arXiv:2504.01307},
year = {2025}
}