Wavelet bases of Hermite cubic splines on the interval |
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Authors: | Rong-Qing Jia Song-Tao Liu |
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Institution: | (1) Department of Math. and Stat. Sciences, University of Alberta, Edmonton, Canada, T6G 2G1 |
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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.
Dedicated to Dr. Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 42C40, 41A15, 65L60.
Research was supported in part by NSERC Canada under Grants # OGP 121336. |
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Keywords: | wavelets on the interval Hermite cubic splines numerical solutions of differential equations |
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