zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Spectral-like resolution compact ADI finite difference method for the multi-dimensional Schrödinger equations. (English) Zbl 1255.81014
Summary: We propose a family of high order compact ADI (HOC-ADI) scheme for multi-dimensional Schrödinger equations. In a specific case, it is of sixth-order accuracy in space. To cut down the computational labor, we adopt ADI strategy in the time direction. Moreover, for nonlinear problem, the second-order standard Strang splitting skill is used. The conservation properties and stability are analyzed for the proposed scheme. Numerical results in 2d and 3d are reported to demonstrate the new spectral-like resolution. Numerical results suggest that the proposed scheme is very efficient and accurate.
MSC:
81-08Computational methods (quantum theory)
81Q05Closed and approximate solutions to quantum-mechanical equations
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)