A numerical technique based on Legendre wavelet for linear and nonlinear hyperbolic telegraph equation

This study is devoted to the numerical investigation of linear and nonlinear hyperbolic telegraph equation. We have proposed a wavelet collocation method based on Legendre polynomials for approximating the solution. Both the spatial and temporal variables, along with their derivatives, are approximated using the Legendre wavelet and its integration. The present approach is simple, consistent and straightforward. To assure the theoretical consistency of the method, an estimate for the upper bound of the error norm is provided. We have proved an exponential order of convergence which is better than the methods available in the literature. Some numerical experiments are carried out to justify the theoretical results and the outcomes confirm the computational efficiency of the proposed method.