In this paper, we first construct third kind Chebyshev wavelets on the interval [0,1). Then, a 2 × 2 matrix P, named as almost third kind Chebyshev wavelets operational matrix of integration is constracted and used to reduce the optimal control problem to a system of algebric equation with the aid of spectral method, which can be solved easily. The uniform convergence of third kind Chebyshev wavelets is also discussed in this paper. The method is then tested on numerical example.
Keywords: Third Kind Chebyshev Polynomials, Wavelets, Optimal Control Problems, Spectral Methed.