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)
A sixth-order compact finite difference method for the one-dimensional sine-Gordon equation. (English) Zbl 1222.65097
Summary: This paper explores the utility of a sixth-order compact finite difference (CFD6) scheme for the solution of the sine-Gordon equation. The CFD6 scheme in space and a third-order strong stability preserving Runge-Kutta scheme in time have been combined for solving the equation. This scheme needs less storage space, as opposed to the conventional numerical methods, and causes to less accumulation of numerical errors. The scheme is implemented to solve three test problems having exact solutions. Comparisons of the computed results with exact solutions showed that the method is capable of achieving high accuracy with minimal computational effort. The present results are also seen to be more accurate than some available results given in the literature. The scheme is seen to be a very reliable alternative technique to existing ones.

MSC:
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35Q40PDEs in connection with quantum mechanics
WorldCat.org
Full Text: DOI