New explicit group iterative methods in the solution of three dimensional hyperbolic telegraph equations

Abstract

In this paper, new group iterative numerical schemes based on the centred and rotated (skewed) seven-point finite difference discretisations are proposed for the solution of a three dimensional second order hyperbolic telegraph equation, subject to specific initial and Dirichlet boundary conditions. Both schemes are shown to be of second order accuracies and unconditionally stable. The scheme derived from the rotated grid stencil results in a reduced linear system with lower computational complexity compared to the scheme derived from the centred approximation formula. A comparative study with other common point iterative methods based on the seven-point centred difference approximation together with their computational complexity analyses is also presented.