A "converse" stability condition is necessary for a compact higher order scheme on non-uniform meshes
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2017
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908741916426240 |
|---|---|
| author | Zlotnik, Alexander Čiegis, Raimondas |
| author_facet | Zlotnik, Alexander Čiegis, Raimondas |
| contents | The stability bounds and error estimates for a compact higher order Numerov-Crank-Nicolson scheme on non-uniform space meshes for the 1D time-dependent Schrödinger equation have been recently derived. This analysis has been done in $L^2$ and $H^1$ mesh norms and used the non-standard "converse" condition $h_ω\leq c_0τ$, where $h_ω$ is the mean space step, $τ$ is the time step and $c_0>0$. Now we prove that such condition is necessary for some families of non-uniform meshes and any space norm. Also numerical results show unacceptably wrong behavior of numerical solutions (their dramatic mass non-conservation) when this condition is violated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1707_09943 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A "converse" stability condition is necessary for a compact higher order scheme on non-uniform meshes Zlotnik, Alexander Čiegis, Raimondas Numerical Analysis 65M06, 65M12 The stability bounds and error estimates for a compact higher order Numerov-Crank-Nicolson scheme on non-uniform space meshes for the 1D time-dependent Schrödinger equation have been recently derived. This analysis has been done in $L^2$ and $H^1$ mesh norms and used the non-standard "converse" condition $h_ω\leq c_0τ$, where $h_ω$ is the mean space step, $τ$ is the time step and $c_0>0$. Now we prove that such condition is necessary for some families of non-uniform meshes and any space norm. Also numerical results show unacceptably wrong behavior of numerical solutions (their dramatic mass non-conservation) when this condition is violated. |
| title | A "converse" stability condition is necessary for a compact higher order scheme on non-uniform meshes |
| topic | Numerical Analysis 65M06, 65M12 |
| url | https://arxiv.org/abs/1707.09943 |