Work

Efficient numerical approximations for a nonconservative nonlinear Schrödinger equation appearing in wind‐forced ocean waves

Year: 2024

Type: article

Abstract: We consider a nonconservative nonlinear Schrödinger equation (NCNLS) with time‐dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy conservation, but instead mass and energy change in time under explicit balance laws. In this paper, we extend to the particular NCNLS two numerical schemes which are known to conserve energy and mass in the discrete level for the cubic nonlinear Schrödinger equation. Both schemes are second‐order accurate in time, and we prove that their extensions satisfy discrete versions of the mass and energy balance laws for the NCNLS. The first scheme is a relaxation scheme that is linearly implicit. The other scheme is a modified Delfour–Fortin–Payre scheme, and it is fully implicit. Numerical results show that both schemes capture robustly the correct values of mass and energy, even in strongly nonconservative problems. We finally compare the two numerical schemes and discuss their performance.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.12774

Authors: Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza

Institutions: University of Dundee, University of Crete, FORTH Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, University of St Andrews

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,330

OpenAlex ID: W4403773360

FWCI: 0.384

Cites: 33

Cited by: 1

Related to: 10