Application of wavelet collocation method for hyperbolic partial differential equations via matrices

In this work, we developed an efficient computational method based on Legendre and Chebyshev wavelets to find an approximate solution of one dimensional hyperbolic partial differential equations (HPDEs) with the given initial conditions. The operational matrices of integration for Legendre and Chebyshev wavelets are derived and utilized to transform the given PDE into the linear system of equations by combining collocation method. Convergence analysis and error estimation associated to the presented idea are also investigated under several mild conditions. Numerical experiments confirm that the proposed method has good accuracy and efficiency. Moreover, the use of Legendre and Chebyshev wavelets are found to be accurate, simple and fast.