Wavelet bases of Hermite cubic splines on the interval
- 176 Downloads
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.
Keywordswavelets on the interval Hermite cubic splines numerical solutions of differential equations
Unable to display preview. Download preview PDF.
- S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods (Springer, New York, 1994). Google Scholar
- C.K. Chui and E. Quak, Wavelets on a bounded interval, in: Numerical Methods in Approximation Theory, Vol. 9, eds. D. Braess and L.L. Schumaker (Birkhäuser, Basel, 1992) pp. 53–75. Google Scholar
- P.G. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation (Cambridge Univ. Press, Cambridge, 1989). Google Scholar
- I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, PA, 1992). Google Scholar
- R.Q. Jia and C.A. Micchelli, Using the refinement equations for the construction of pre-wavelets II: Powers of two, in: Curves and Surfaces, eds. P.J. Laurent, A. Le Méhauté and L.L. Schumaker (Academic Press, New York, 1991) pp. 209–246. Google Scholar
- Y.J. Shen and W. Lin, A wavelet-Gelerkin method for a linear equation system with Hadamard integrals, manuscript. Google Scholar