Efficient orthogonal spline collocation methods for solving linear second order hyperbolic problems on rectangles (Q1363211)

The author analyzes certain spline and alternating directions schemes for the approximate solution of linear second-order hyperbolic problems on rectangles. The schemes in question are shown to be unconditionally stable in \(H^1\) and discrete maximum norms in space and time. Implementations and numerical results are presented in some detail. The methods used are orthogonal spline collocation counterparts of finite element Galerkin-Laplace modified methods and alternating direction implicite difference schemes, which have previously been treated by the author (partly jointly with G. Faiweather).