Year: 2025
Type: article
Abstract: ABSTRACT We construct second‐order structure‐preserving two‐step linearly implicit exponential integrators for Hamiltonian partial differential equations with linear constant damping combining discrete gradient methods and polarization of the polynomial Hamiltonian function. We also construct an exponential version of the well‐known one‐step Kahan's method by polarizing the quadratic vector field. These integrators are applied to one‐dimensional damped Burger's, Korteweg‐de Vries, and nonlinear Schrödinger equations. Preservation of the dissipation rate is demonstrated for linear and quadratic conformal invariants and for the Hamiltonians by numerical experiments.
DOI: 10.1002/mma.70174
Authors: Murat Uzunca, Bülent Karasözen
Institutions: Sinop University, Middle East Technical University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $5,000
OpenAlex ID: W4414678574