zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
High order compact solution of the one-space-dimensional linear hyperbolic equation. (English) Zbl 1151.65071

Summary: We introduce a high-order accurate method for solving one-space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivative of linear hyperbolic equation and collocation method for the time component. The main property of this method additional to its high-order accuracy due to the fourth order discretization of spatial derivative, is its unconditionally stability. In this technique the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations.

Numerical results show that the compact finite difference approximation of fourth order and collocation method produce a very efficient method for solving the one-space-dimensional linear hyperbolic equation. We compare the numerical results of this paper with numerical results of R. K. Mohanty [Appl. Math. Lett. 17, No. 1, 101–105 (2004; Zbl 1046.65076)].

65M06Finite difference methods (IVP of PDE)
65M70Spectral, collocation and related methods (IVP of PDE)
35L15Second order hyperbolic equations, initial value problems