Group-Based BCU–Exit Method
The correctness of the controlling unstable equilibrium point (controlling UEP, or CUEP) computed by the BCU method can be verified by checking the boundary property rather than by checking the one-parameter transversality condition. By computing the boundary distance of the computed unstable equilibrium point (UEP), one can verify whether the boundary property is satisfied. If the boundary distance of the computed UEP is 1.0, then the boundary property is satisfied; otherwise, it is not. It has been shown that the BCU method computes the correct CUEP if the boundary property is satisfied. When the boundary property is not satisfied, the BCU–exit point should be computed and its energy value will give the accurate critical energy. Since the tasks of verifying the boundary property and computing the BCU–exit point are rather time-consuming, the exploration of some group properties will prove very useful in reducing the required computational effort.
The boundary property is a group property. It is therefore unnecessary to compute the boundary distance of every computed UEP (relative to a contingency) in a group of coherent contingencies. Instead, it is sufficient to compute the boundary distance of a selected UEP in a group of coherent contingencies and to check the boundary property for all contingencies in that group. If a group of coherent contingencies does not satisfy the boundary property, then the UEPs computed ...