Solution of differential equations via Chebyshev Operational matrix of integration

Abstract

In this paper, operational matrices for integration and product operations of
the fourth kind Chebyshev wavelets are constructed. These matrices are utilized to obtain
solutions to linear differential equations, which indicate that these matrices are applicable
for fourth kind Chebyshev wavelets. Solutions of the differential equations considered in this
paper, resemble with their exact solutions. The characteristics of fourth kind Chebyshev
wavelets are utilized to transform differential equations to the systems of algebraic equations,
which are solved very efficiently using appropriate methods.