Discrete-Time Orthogonal Spline Collocation Methods for Vibration Problems

Discrete-time orthogonal spline collocation schemes are formulated and analyzed for vibration problems involving various boundary conditions. Each problem is written as a Schrodinger-type system, which is then approximated by Crank--Nicolson and/or alternating direction implicit orthogonal spline collocation schemes. These schemes are shown to be second-order accurate in time and of optimal order accuracy in space in the Hm-norm, m=1,2.