2023/09/25 by Murat Uzunca, Uzunca, Murat, Bülent Karasözen +1
Computer Science · Engineering · Mathematics · #Control and Stability of Dynamical Systems #FOS: Mathematics #Modeling and Simulation Systems #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2309.14184
openalex publication_date 2023/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the Hamiltonian function and portioning out the nonlinearly of consecutive time steps. They require only a solution of one linear system at each time step. Therefore they are computationally more advantageous than implicit integrators. 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 of linear and quadratic conformal invariants and the Hamiltonian is illustrated by numerical experiments.