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

Abstract

In this paper, we present the development of new explicit group relaxation methods which solve the two dimensional second order hyperbolic telegraph equation subject to specific initial and Dirichlet boundary conditions. The explicit group methods use small fixed group formulations derived from a combination of the rotated five-point finite difference approximation together with the centered five-point centered difference approximation on different grid spacings. The resulting schemes involve three levels finite difference approximations with second order accuracies. Analyses are presented to confirm the unconditional stability of the difference schemes. Numerical experimentations are also conducted to compare the new methods with some existing schemes.