SIAM Journal on Numerical Analysis · 2002 · 25 citations · 8 references
ComputingComputational EngineeringMechanical EngineeringComputational MechanicsStructural DynamicsVibrationApproximation MethodsConvergence AnalysisFinite Element DiscretizationNumerical AlgorithmsNumerical Methods For Differential EquationsVibration AnalysisComputational Vibration AnalysisNumerical Solution Of The Schrödinger EquationOrder AccuracySpline ApproximationTruncation ErrorVibrational Analysis
Discrete-time orthogonal spline collocation schemes are formulated and analyzed for vibration problems involving various boundary conditions. Each problem is written as a Schrödinger-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.
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