Comparative work for the source identification in parabolic inverse problem based on Taylor and Chebyshev wavelet methods

Abstract

In this article, we study wavelet collocation methods based on Taylor and Chebyshev wavelets for source identification in the parabolic inverse problem. In the proposed method, the highest order derivative is written in terms of the 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 the Taylor wavelet method provides us with a better result than the Chebyshev wavelet method. CPU time has also been shown to ensure the efficiency of the method.