On the Use of Implicit and Iterative Methods for the Time Integration of the Wave Equation

The numerical properties of the trapezoidal implicit, the backward implicit, and partly implicit methods are investigated. The computational stability of these methods, the selective damping of waves, and the accuracy of the predicted wave are discussed primarily for wave equations in the simple form. Then, their applicability to the integration of the primitive equations is considered for a system of linearized equations. The characteristic features of four iterative methods, each of which consists of a predictor and a corrector to be used only once, are also described.