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)
Finite difference approximate solutions for the Rosenau equation. (English) Zbl 0904.65093

Numerical solutions of a finite difference scheme are discussed for the KdV-like Rosenau equation

u t +u xxxxt +uu x +u x =0,(x,t)(0,1)×(0,T]

with an initial condition

u(x,0)=u 0 (x),x(0,1)

and boundary conditions

u(0,t)=u(1,t)=0,u xx (0,t)=u xx (1,t)=0·

This equation was modelled by P. Rosenau [Dynamics of dense discrete systems, Prog. Theoretical Phys. 79, 1028-1042 (1988)] in order to describe the dynamics of dense discrete systems.

Existence and uniqueness of the solution for the scheme are shown by using the Brouwer fixed point theorem. An a priori bound and convergence of order O(h 2 +k 2 ) as well as conservation of energy of the finite difference approximate solutions are discussed with numerical examples.

MSC:
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations