A variational method using Alpert multiwavelets

Stacey, A and Blyth, W 2008, 'A variational method using Alpert multiwavelets', The ANZIAM Journal, vol. 48, pp. C820-C836.


Document type: Journal Article
Collection: Journal Articles

Title A variational method using Alpert multiwavelets
Author(s) Stacey, A
Blyth, W
Year 2008
Journal name The ANZIAM Journal
Volume number 48
Start page C820
End page C836
Publisher Cambridge University Press
Abstract The numerical solution of variational problems is usually achieved by numerical solution of the Euler-Lagrange differential equations or by Rayleigh-Ritz direct methods (in which the Euler-Lagrange equations are not used). In 1975, Chen and Hsiao showed how Walsh functions could be used in a direct method to solve two model variational problems. This Rayleigh-Ritz method was generalized by Sloss and Blyth in 1998. In 2004, Hsiao modified the Walsh function method to provide a Haar wavelet direct method and illustrated how this can be used for the solution of a few model problems. In this paper Alpert multiwavelets are applied to the direct solution of variational problems. Alpert multiwavelets were developed for the numerical solution of integral equations and provide a generalization of the simpler Haar wavelets that have already been successfully employed in the solution of integral equations. Alpert multiwavelets have the advantage of being expressible as simple polynomials over disjoint subintervals allowing for ease of computation. The method is applied to a number of examples which allow comparisons with the results for Haar wavelets. Some convergence results are also be given.
Subject Numerical Solution of Differential and Integral Equations
Copyright notice © Australian Mathematical Society, 2008
ISSN 1446-1811
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