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On the Galerkin-Wavelet method for higher order differential equations

Naohiro Fukuda|Tomatu Kinoshita|Takatuki Kubo
대한수학회 (The Korean Mathematical Society)|2013.05|대한수학회보 (Bulletin of the KMS)|제50권 제3호|pp. 963-982

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참고문헌

키워드

Riesz basisGalerkin-wavelet methodhigher order differential equation
주제분류수학

초록

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 Vj ⊂ L2. 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.

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 Vj ⊂ L2. 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.

참고문헌 (17)

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  11. E. Hern´andez, "A First Course on Wavelets" (1996), CRC Press
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  13. H. C. Martin, "Introduction to Finite Element Analysis" (1973), McGraw-Hill Book Co.
  14. J. O. Stromberg, "A modified Franklin system and higher-order spline systems on Rn as unconditional bases for Hardy spaces", Conference on harmonic analysis in honor of Antoni Zygmund, pp.475~494 (1981)
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