Convergence analysis of an efficient Chebyshev wavelet and its applications to differential equations via operational matrices of integration

In this paper, the convergence analysis of the Chebyshev wavelet of the second kind is thoroughly carried out. Operational matrices for integration and product operations of the second kind Chebyshev wavelet are constructed, and these matrices are utilized to obtain solutions to the differential equations. A theorem related to the proposed operational matrix method is established. Solutions of the differential equations considered in this paper resemble their exact solutions. The characteristics of second kind Chebyshev wavelet are utilized to transform differential equations into systems of algebraic equations, which are solved very efficiently using a suitable method.