Numerical computation method in solving integral equations by using Chebyshev wavelet operational matrix of integration

A direct method for solving integral equations whose solutions are continuous or discontinuous by using Chebyshev wavelet basis in Galerkin equations is presented. Another method for solving Volterra type integral equations which use operational matrix of integration (OMI) for Chebyshev wavelets is introduced and used to reduce this type of integral equations to a system of algebraic equations. Some quadrature formula for calculating inner products have presented which can be operated by fast Fourier transform (FFT). The numerical examples and the number of operations show the advantages of Chebyshev Wavelet Galerkin method to some other usual methods and usual Chebyshev basis.