Alternating Direction Methods for Hyperbolic Differential Equations

Abstract

The difference equation (1.1) u_(tt) = u_(xx) + η/k^2u_(xxtt)
\ndepending on the nonnegative parameter η, was introduced by von Neumann (cf. [1]) for the numerical solution of boundary value problems for the one-dimensional wave equation ∂^2w/∂t^2 = ∂^2w/∂x^2.