The existence and uniqueness of solution to wavelet collocation

The study of the numerical solutions of PDEs with wavelet collocation has yielded a number of substantial results. However, the existence and uniqueness of solution has not been discussed yet. In this paper, the existence and uniqueness of solution to wavelet collocation for elliptic equations is established and discussed. Moreover, wavelet collocation is applied to numerical example to examine its appropriateness. According to numerical example and analysis, it is seen that the existence and uniqueness of solution of this paper is feasible, and the new theory is meaningful for developing wavelet collocation.