Abstract:

The study of the numerical solutions of PDEs with wavelet collocation has yielded a number of substantial results. However, the existence and uniqueness of the solution has not been discussed. The existence and uniqueness of the solution of parabolic equations with wavelet collocation are established and discussed, where its explicit scheme and implicit scheme are given. Also, wavelet collocation is applied to parabolic equations to examine its appropriateness.
 

Key words: wavelet collocation; parabolic equations; the existence and uniqueness of the solution