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Bull. Korean Math. Soc. 2013; 50(3): 963-982

Printed May 31, 2013

https://doi.org/10.4134/BKMS.2013.50.3.963

Copyright © The Korean Mathematical Society.

On the Galerkin-Wavelet method for higher order differential equations

Naohiro Fukuda, Tamotu Kinoshita, and Takayuki Kubo

University of Tsukuba, University of Tsukuba, University of Tsukuba

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The Galerkin method has been developed mainly for 2nd order differential equations. To get numerical solutions, there are some choices of Riesz bases for the approximation subspace $V_j \subset L^2$. In this paper we shall propose a uniform approach to find suitable Riesz bases for higher order differential equations. Especially for the beam equation ($4$-th order equation), we also report numerical results.

Keywords: Galerkin-wavelet method, Riesz basis, higher order differential equation

MSC numbers: 65N30, 65L60, 80M10

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