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)-∫01K(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 C1 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.