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

TL;DR

This paper compares Taylor and Chebyshev wavelet methods for source identification in parabolic inverse problems, demonstrating that Taylor wavelets yield more accurate results and are computationally efficient.

Contribution

It introduces a wavelet collocation approach using Taylor and Chebyshev wavelets for inverse source identification, with a convergence analysis and comparative numerical results.

Findings

Taylor wavelet method provides better accuracy than Chebyshev wavelet method.

The proposed methods are computationally efficient.

Numerical results confirm the effectiveness of the Taylor wavelet approach.

Abstract

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.