A New Technique to Speed Up Group Methods for Solving Hyperbolic Telegraph Equations (European Journal of Pure and Applied Mathematics, 2021)
Numerous methods have been introduced in the literature for numerical solution of two-dimensional hyperbolic differential equations (telegraph equations). Improved techniques using explicit group methods derived from the standard and skewed (rotated) finite difference operators have been developed over the last few years in solving the linear systems that arise from the discretization of the several types of partial differential equations. In this paper, we present a preliminary study of the formulation of new preconditioned scheme based on explicit group relaxationmethods for the difference solution of the telegraph equations. The efficient and robustness of these new formulations over the existing explicit group schemes demonstrated through numerical experiments.
Keywords: Preconditioned technique; Finite difference method; Group iterative method; Telegraph Equations.