Efficient orthogonal spline collocation methods for solving linear second order hyperbolic problems on rectangles
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).
finite element Galerkin-Laplace modified methods
alternating direction implicite difference schemes
scientific article; zbMATH DE number 1049543