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Wavelet bases of Hermite cubic splines on the interval

By Rong-qing Jia and Song-tao Liu

Abstract

In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C1 and supported on [−1, 1]. Moreover, one wavelet is symmetric, and the other is antisymmetric. These spline wavelets are then adapted to the interval [0, 1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of the wavelet basis is established. The wavelet basis is used to solve the Sturm–Liouville equation with the Dirichlet boundary condition. Numerical examples are provided. The computational results demonstrate the advantage of the wavelet basis

Topics: wavelets on the interval, Hermite cubic splines, numerical solutions of differential equations
Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.2668
Provided by: CiteSeerX
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