A Crank–Nicolson orthogonal spline collocation method for vibration problems Original Research Article

A discrete-time orthogonal spline collocation scheme is formulated and analyzed for a problem governing the transverse vibrations of a clamped square plate. The problem is reformulated as a Schrödinger-type system which is then approximated by a Crank–Nicolson orthogonal spline collocation scheme. This scheme is shown to be second-order accurate in time and of optimal order accuracy in space in the H1- and H2-norms.