Wavelet numerical solutions for weakly singular Fredholm integral equations of the second kind
Xinjian Tang, Zhicheng Pang, Tonglin Zhu, Jian Liu · Wuhan University Journal of Natural Sciences · 2007
Daubechies interval wavelet is used to solve numerically weakly singular Fredholm integral equations of the second kind. Utilizing the orthogonality of the wavelet basis, the integral equation is reduced into a linear system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse, while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally, numerical example is presented to show the application of the wavelet method.