A family of structure-dependent integration methods has been proposed by Gui et al. for time integration. Although it has desirable numerical properties, such as unconditional stability, explicit formulation and second-order accuracy, it has some adverse properties, such as a poor capability to capture structural nonlinearity, an overshoot in a high frequency steady- state response and a weak instability in the high frequency response of nonzero initial conditions. The causes of these adverse properties are explored. A poor capability to capture structural nonlinearity may originate from the convergence rate of 1 in velocity error. This family method has an overshoot in a high frequency steady-state response and this overshoot can be eliminated by adding a load-dependent term into the displacement difference equation. It is also analytically verified that the family method generally has no weak instability. However, the special member with λ = 4, i.e., CR explicit method, is shown to have a weak instability. Thus, it must be prohibited from practical applications although many applications of this method were found in the literature.

This article examines the impacts of monetary policy on agricultural prices in four Asian economies using time series analysis and graph theory. The estimations clearly show that agricultural prices overshoot their long-run equilibrium values for Korea, Philippines, and Thailand, and the overshooting for agricultural prices is larger than for manufactured prices. Impulse-response functions and variance-decomposition analysis based on directed graphs and causal structures highlight the complex interplay among the variables in the model and how those relationships differ by country. Money supply changes clearly affect real variables and relative prices for all countries either through overshooting or non-neutrality of money.

As compressible convection has inherent up/down asymmetry, overshooting above and below a convection zone behave differently. In downward overshooting, the narrow down-flow columns dynamically play an important role. It is customary, and reasonable, to use the downward flux of kinetic energy as a proxy for overshooting. In the upward situation, the flux of kinetic energy can take on different signs near the upper boundary of the convection zone, and its magnitude is generally small. It cannot make a good proxy for overshooting. This paper discusses the results of a set of numerical experiments that investigate the problem of overshooting above a convection zone. Particle tracing and color advection are used to follow the mixing process. The overshoot region above a convection zone is found to contain multiple counter cell layers.