Error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations (Q1108756)

In an earlier paper [ibid. 12A, 581-604 (1986; Zbl 0596.65079)] the author considered the problem: \[ (1)\quad u_{tt}=\sum^{N}_{j,k=1}\partial /\partial x_ j[a_{j_ k}(x,t,u)\partial u/\partial x_ k]-a_ 0(x,t,u)u+f(x,t,u,u_ t,\nabla u) \] u\(=0\) in \(\Omega\) \(\times [0,\tau]\) \(u(0)=u^ 0\), \(u_ t(0)=u^ 0_ t\) in \(\Omega\), where \(\Omega\) is bounded in \(R^ N\), \(1\leq N\leq 3\) when f is independent of \(u_ t\) and u. The aim of the present paper is to give single step methods for numerically solving the more general case (1).