Use this URL to cite this publication: https://hdl.handle.net/20.500.14911/119119
A "converse'' stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation
Publication Type (CRIS)
Straipsnis Web of Science ir Scopus duomenų bazėje / Article in Web of Science and Scopus database (S1)
Publication Type (eLABa)
Straipsnis Web of Science DB / Web of Science DB article (S1)
VILNIUS TECH Research Priorities and Topics
Fizinių, technologinių ir ekonominių procesų matematiniai modeliai ir metodai / Mathematical models and methods of physical, technological and economic processes (FM03)
Lithuanian Intelligent Specialization
Įtrauki ir kūrybinga visuomenė / Inclusive and creative society (L103)
Author(s)
| Author | Affiliation |
|---|---|
Zlotnik, Aleksandr | National Research University Higher School of Economics, Moscow, Russia |
Title
A "converse'' stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation
Aleksandr Zlotnik, Raimondas Čiegis
Is part of
Applied mathematics letters
Published In
| Year | Volume | Start Page | End Page |
|---|---|---|---|
2018 | 80 | 35 | 40 |
Publisher
Oxford : Elsevier
Publisher (trusted)
Extent
p. 35-40
URI
| URI | Access Rights |
|---|---|
| https://hdl.handle.net/20.500.14911/119119 | |
| Straipsnis | Viso teksto dokumentas (atviroji prieiga) / Full Text Document (Open Access) |
Cited references
13
Science / Art Area
Gamtos mokslai / Natural Sciences (N)
Field of Science / Art
Matematika / Mathematics (N001)
Abstract (en)
The stability bounds and error estimates for a compact higher order Numerov-Crank-Nicolson scheme on non-uniform spatial meshes for the 1D time-dependent Schrödinger equation have been recently derived. This analysis has been done in L2 and H1 mesh norms and used the non-standard "converse'' condition hw ≤ c0Ƭ, where hw is the mean spatial step, Ƭ is the time step and c0>0. Now we prove that such condition is necessary for some families of non-uniform meshes and any spatial norm. Also computational results for zero and non-zero potentials show unacceptably wrong behavior of numerical solutions when Ƭ decreases and this condition is violated.
Resource Type (COAR)
TextJournalJournal articleResearch article
Language
Anglų / English (en)
Country
Jungtinė Karalystė / United Kingdom of Great Britain and Northern Ireland (GB)
Owning collection
ISSN (of the container)
0893-9659
WOS
000427219100006
Scopus
2-s2.0-85041472208
eLABa ID
25873351
Project(s)
Academic Fund Program at the National Research University Higher School of Economics
Russian Academic Excellence Project '5-100'