论文信息 - Numerical solution of the integral equation of the second kind by using wavelet bases of Hermite cubic splines

Numerical solution of the integral equation of the second kind by using wavelet bases of Hermite cubic splines

In this paper, We use the wavelet bases of Hermite cubic splines to solve the second kind integral equationsx(t)-@!"0^1K(t,s)x(s)ds=y(t),t@?[0,1].A pair of wavelets are constructed on the basis of Hermite cubic splines. This wavelets are in C^1 and supported on [0,2]. Moreover, one wavelet is symmetric, and the other is anti-symmetric. This spline wavelets are then adapted to the interval [0,1]. The computational results demonstrate the advantage of the wavelet basis.

Khosrow Maleknejad | Mehdi Yousefi | K. Maleknejad | M. Yousefi

[1] L. Delves,et al. Computational methods for integral equations: Frontmatter , 1985 .

[2] G. Strang,et al. Approximation by translates of refinable functions , 1996 .

[3] I. Daubechies,et al. Wavelets on the Interval and Fast Wavelet Transforms , 1993 .

[4] C. Chui,et al. On compactly supported spline wavelets and a duality principle , 1992 .

[5] George C. Donovan,et al. Construction of Orthogonal Wavelets Using Fractal Interpolation Functions , 1996 .

[6] W. Dahmen,et al. Biorthogonal Multiwavelets on the Interval: Cubic Hermite Splines , 2000 .

[7] L. Delves,et al. Numerical solution of integral equations , 1975 .

[8] Rong-Qing Jia,et al. Wavelet bases of Hermite cubic splines on the interval , 2006, Adv. Comput. Math..

[9] L. Schumaker,et al. Numerical methods in approximation theory , 1992 .

[10] P. Kythe,et al. Computational Methods for Linear Integral Equations , 2002 .

[11] K. Atkinson. The Numerical Solution of Integral Equations of the Second Kind , 1997 .

[12] Fritz Keinert,et al. Wavelets and Multiwavelets , 2003 .

[13] C. Chui,et al. Wavelets on a Bounded Interval , 1992 .

[14] Jianzhong Wang,et al. CUBIC SPLINE WAVELET BASES OF SOBOLEV SPACES AND MULTILEVEL INTERPOLATION , 1996 .