On the Galerkin-Wavelet method for higher order differential equations
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 963-982
Printed May 31, 2013
Naohiro Fukuda, Tamotu Kinoshita, and Takayuki Kubo
University of Tsukuba, University of Tsukuba, University of Tsukuba
Abstract : 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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