An Efficient Computational Approach Based on Chebyshev Wavelets for Two‐Dimensional Hyperbolic Telegraph Equation With Convergence Analysis

In this paper, Chebyshev wavelets method is designed and presented to approximate the two‐dimensional (2D) telegraph equation of hyperbolic type. Firstly, we transform the original problem into the equivalent integro‐partial differential equations (integro‐PDEs) containing the initial and boundary conditions. Thereafter, the operational matrices of integration and derivative of Chebyshev wavelets reduce the integro‐PDEs into generalized Sylvester equations which are solved by Krylov subspace iterative method. The convergence analysis associated to the function approximation, and error estimation are also investigated. The presented procedure is found to be very effective and accurate, which is confirmed by the outcome of three test examples. The outcome of numerical results of errors achieved by the presented method is compared with some earlier works. The technique can be applied for higher dimension problems also, which is one of the key features of this technique.