Five-diagonal finite difference methods based on mixed-type interpolation for a certain fourth-order two-point boundary-value problem
type: Item
instance of: scholarly article
title: Five-diagonal finite difference methods based on mixed-type interpolation for a certain fourth-order two-point boundary-value problem
zbMATH Open document ID: 0770.65053
DOI: 10.1016/0898-1221(92)90019-E
publication date: 1993-02-22T00:00:00Z
review text: This paper derives various mixed-type interpolational formulas based on a linear combination of a polynomial of degree \(q-2\) and a (hyperbolic) cosine and (hyperbolic) sine function of the same frequency \((k)\) for solving fourth order, two-point boundary value problems directly. Such methods are of order \(q+1\) and their implementation leads to the solution of 5-diagonal linear systems of equations. The frequency value is treated as a free parameter. In the case \(k=0\) the methods reduce to those of \textit{R. A. Usmani} [Indian J. Pure Appl. Math. 14, 398-411 (1983; Zbl 0522.65054)]. The authors prove that truncation errors are of the form \(k^ 2y^{(q+3)}(\xi)+y^{(q+5)}(\xi)\) and suggest choosing \(k^ 2\) so that this term is zero. This is done by approximating these derivatives by second or fourth order schemes. Numerical results indicate an \(O(h^ 2)\) improvement for these methods over Usmani's methods of the same order.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 120300
zbMATH Keywords: five-diagonal finite difference methods
zbMATH Keywords: mixed interpolation
zbMATH Keywords: fourth order, two-point boundary value problems
zbMATH Keywords: Numerical results
author: M. Van Daele
author: G. Vanden Berghe
author: H. De Meyer
reviewed by: Kevin Burrage
describes a project that uses: MACSYMA
MaRDI profile type: Publication
cites work: Finite difference methods for a certain two point boundary value problem
cites work: Q5574370
cites work: On a new type of mixed interpolation
cites work: On the error estimation for a mixed type of interpolation
cites work: Q5674335
cites work: Q5330830
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 120300