  In this article, we study wavelet collocation methods based on Taylor and
Chebyshev wavelets for the source identification in parabolic inverse problem.
In the proposed method, highest order derivative is written in terms of Taylor
and Chebyshev wavelet series and required unknown terms are obtained using
successive integration. Taylor series approximation has been utilized to obtain
the source control parameter. Convergence analysis is carried out in order to
guarantee the accuracy of the method. Numerical results have been obtained
based on the proposed methods and it is shown that Taylor wavelet method
provide us better result than the Chebyshev wavelet method. CPU time has also
been shown to ensure the efficiency of the method.
