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Title: Differential quadrature solutions of eighth-order boundary-value differential equations
Authors: Liu, G.R. 
Wu, T.Y.
Keywords: Collocation method
Differential quadrature method
Eighth-order boundary-value problem
Finite difference method
Hydrodynamic stability
Numerical method
Pseudospectral method
Issue Date: 1-Aug-2002
Citation: Liu, G.R., Wu, T.Y. (2002-08-01). Differential quadrature solutions of eighth-order boundary-value differential equations. Journal of Computational and Applied Mathematics 145 (1) : 223-235. ScholarBank@NUS Repository.
Abstract: Special cases of linear eighth-order boundary-value problems have been solved using polynomial splines. However, divergent results were obtained at points adjacent to boundary points. This paper presents an accurate and general approach to solve this class of problems, utilizing the generalized differential quadrature rule (GDQR) proposed recently by the authors. Explicit weighting coefficients are formulated to implement the GDQR for eighth-order differential equations. A mathematically important by-product of this paper is that a new kind of Hermite interpolation functions is derived explicitly for the first time. Linear and non-linear illustrations are given to show the practical usefulness of the approach developed. Using Frechet derivatives, non-linear eighth-order problems are also solved for the first time. Numerical results obtained using even only seven sampling points are of excellent accuracy and convergence in an entire domain. The present GDQR has shown clear advantages over the existing methods and demonstrated itself as a general, stable, and accurate numerical method to solve high-order differential equations. © 2001 Elsevier Science B.V. All rights reserved.
Source Title: Journal of Computational and Applied Mathematics
ISSN: 03770427
DOI: 10.1016/S0377-0427(01)00577-5
Appears in Collections:Staff Publications

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