Group explicit methods for hyperbolic equations (Q1107281)

Here the group explicit (GE) method which was introduced by the first author and \textit{A. R. B. Abdullah} [Int. J. Comput. Math. 14, 73-105 (1983; Zbl 0517.65069)] to solve parabolic partial differential equations is extended to hyperbolic equations of the first and second order. The GE method involves the use of asymmetric approximations to derivatives in different mesh points. These are then couples in groups of two adjacent points in such a way that a certain cancellation of errors in the numerical solution of the differential equation occurs. The presentation of the algorithm is followed by theoretical aspects on the stability, consistency, convergence and truncation errors.