High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperbolization
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915557487411200 |
|---|---|
| author | Ranocha, Hendrik Ketcheson, David I. |
| author_facet | Ranocha, Hendrik Ketcheson, David I. |
| contents | We propose a class of numerical methods for the nonlinear Schrödinger (NLS) equation that conserves mass and energy, is of arbitrarily high-order accuracy in space and time, and requires only the solution of a scalar algebraic equation per time step. We show that some existing spatial discretizations, including the popular Fourier spectral method, are in fact energy-conserving if one considers the appropriate form of the energy density. We develop a new relaxation-type approach for conserving multiple nonlinear functionals that is more efficient and robust for the NLS equation compared to the existing multiple-relaxation approach. The accuracy and efficiency of the new schemes is demonstrated on test problems for both the focusing and defocusing NLS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperbolization Ranocha, Hendrik Ketcheson, David I. Numerical Analysis 65M12, 65M70, 65M06, 65M60, 65M20 We propose a class of numerical methods for the nonlinear Schrödinger (NLS) equation that conserves mass and energy, is of arbitrarily high-order accuracy in space and time, and requires only the solution of a scalar algebraic equation per time step. We show that some existing spatial discretizations, including the popular Fourier spectral method, are in fact energy-conserving if one considers the appropriate form of the energy density. We develop a new relaxation-type approach for conserving multiple nonlinear functionals that is more efficient and robust for the NLS equation compared to the existing multiple-relaxation approach. The accuracy and efficiency of the new schemes is demonstrated on test problems for both the focusing and defocusing NLS. |
| title | High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperbolization |
| topic | Numerical Analysis 65M12, 65M70, 65M06, 65M60, 65M20 |
| url | https://arxiv.org/abs/2510.14335 |