Efficient spectral ultraspherical-dual-Petrov–Galerkin algorithms for the direct solution of (2n+1)th-order linear differential equations

E.H. Doha and W.M. Abd-Elhameed

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 11, 3221-3242

Abstract: Some efficient and accurate algorithms based on ultraspherical-dual-Petrov–Galerkin method are developed and implemented for solving (2n+1)th-order linear elliptic differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a spectral discretization. The key idea to the efficiency of our algorithms is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results are presented to demonstrate the efficiency of our proposed algorithms.

Keywords: Dual-Petrov–Galerkin method; Ultraspherical polynomials; Nonhomogeneous Dirichlet conditions (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475409001013
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:11:p:3221-3242

DOI: 10.1016/j.matcom.2009.03.011

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().