Numerical solution of two dimensional time-fractional telegraph equation using Chebyshev spectral collocation method

The 2D telegraph equation has numerous applications, such as signal processing, diffusion of biological species, and modeling wave propagation in electrical transmission lines. In this article, we present an efficient numerical scheme for solving the 2D time-fractional telegraph equation using a hybrid approach coupling the Laplace transform (LT) with the spectral collocation method based on Chebyshev nodes (ChSCM). The inclusion of the Caputo derivative in the classical telegraph equation provides a more accurate model for representing anomalous diffusion and wave propagation in heterogeneous media. The LT is employed to handle the time variable, transforming the considered equation into a system of spatial equations. These are then efficiently solved using the ChSCM. In the final step of our suggested approach, the numerical inversion of LT is performed to recover the solution in the time domain. This hybrid approach results in an efficient and robust numerical method. The convergence, accuracy, and stability of the method are verified using numerical examples. The acquired results show the potential of this numerical scheme for approximating the 2D time-fractional partial differential equations.