Abstarct: Classic solutions to partial differential equations have not always been possible and in many cases almost impossible. Therefore, approximate methods should be used to solve this set of equations. In this thesis, we extend an effective method baxsed on Legendre and Chebyshev wavelets to find the approximate solution of partial differential equations with the given initial conditions. In this method, we obtain the integral operator matrices for Legendre and Chebyshev wavelets, and by combining the collocation method convert into a system of linear equations. We also survey the convergence analysis and the corresponding error estimates for these methods under the given conditions and illustrate the accuracy and efficiency of method by providing some examples.