Convergence Analysis of an efficient Chebyshev Wavelet and its Applications to Differential Equations using OMI method

Abstract

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