| dc.contributor.author | Zlotnik, Aleksandr | |
| dc.contributor.author | Čiegis, Raimondas | |
| dc.date.accessioned | 2023-09-18T17:01:51Z | |
| dc.date.available | 2023-09-18T17:01:51Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0893-9659 | |
| dc.identifier.uri | https://etalpykla.vilniustech.lt/handle/123456789/119119 | |
| dc.description.abstract | 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. | eng |
| dc.format | PDF | |
| dc.format.extent | p. 35-40 | |
| dc.format.medium | tekstas / txt | |
| dc.language.iso | eng | |
| dc.relation.isreferencedby | SciSearch | |
| dc.relation.isreferencedby | Zentralblatt MATH (zbMATH) | |
| dc.relation.isreferencedby | Scopus | |
| dc.relation.isreferencedby | ScienceDirect | |
| dc.relation.isreferencedby | Current Contents / Physical, Chemical & Earth Sciences | |
| dc.relation.isreferencedby | Science Citation Index Expanded (Web of Science) | |
| dc.source.uri | https://doi.org/10.1016/j.aml.2018.01.005 | |
| dc.subject | FM03 - Fizinių, technologinių ir ekonominių procesų matematiniai modeliai ir metodai / Mathematical models and methods of physical, technological and economic processes | |
| dc.title | A "converse'' stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation | |
| dc.type | Straipsnis Web of Science DB / Article in Web of Science DB | |
| dcterms.references | 13 | |
| dc.type.pubtype | S1 - Straipsnis Web of Science DB / Web of Science DB article | |
| dc.contributor.institution | National Research University Higher School of Economics, Moscow, Russia | |
| dc.contributor.institution | Vilniaus Gedimino technikos universitetas | |
| dc.contributor.faculty | Fundamentinių mokslų fakultetas / Faculty of Fundamental Sciences | |
| dc.subject.researchfield | N 001 - Matematika / Mathematics | |
| dc.subject.ltspecializations | L103 - Įtrauki ir kūrybinga visuomenė / Inclusive and creative society | |
| dc.subject.en | stability | |
| dc.subject.en | non-uniform spatial mesh | |
| dc.subject.en | compact scheme | |
| dc.subject.en | Numerov-Crank-Nicolson scheme | |
| dc.subject.en | time-dependent Schrödinger equation | |
| dcterms.sourcetitle | Applied mathematics letters | |
| dc.description.volume | Vol. 80 | |
| dc.publisher.name | Elsevier | |
| dc.publisher.city | Oxford | |
| dc.identifier.doi | 000427219100006 | |
| dc.identifier.doi | 2-s2.0-85041472208 | |
| dc.identifier.doi | 10.1016/j.aml.2018.01.005 | |
| dc.identifier.elaba | 25873351 | |
