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As in many-integrator backstepping, the single-step procedure can be completed iteratively to stabilize an entire strict-feedback system. In each step, The smallest "unstabilized" single-step strict-feedback system is isolated. Feedback is used to convert the system into a single-integrator system. The resulting single-integrator system is ...
is used. This well-known method was published by the German mathematician Wilhelm Kutta in 1901, after Karl Heun had found a three-step one-step method of order 3 a year earlier. [19] The construction of explicit methods of even higher order with the smallest possible number of steps is a mathematically quite demanding problem.
Single-step methods (such as Euler's method) refer to only one previous point and its derivative to determine the current value. Methods such as Runge–Kutta take some intermediate steps (for example, a half-step) to obtain a higher order method, but then discard all previous information before taking a second step. Multistep methods attempt ...
Following is a step by step description of the algorithm execution for a small example graph. The source vertex is the vertex A and the radius of every vertex is equal to 1. At the beginning of the algorithm, all vertices except for the source vertex A have infinite tentative distances, denoted by in the pseudocode.
For such problems, to achieve given accuracy, it takes much less computational time to use an implicit method with larger time steps, even taking into account that one needs to solve an equation of the form (1) at each time step. That said, whether one should use an explicit or implicit method depends upon the problem to be solved.
Where the computing systems are duplicated, but both actively process each step, it is difficult to arbitrate between them if their outputs differ at the end of a step. For this reason, it is common practice to run DMR systems as "master/slave" configurations with the slave as a "hot-standby" to the master, rather than in lockstep.
In chemistry, a concerted reaction is a chemical reaction in which all bond breaking and bond making occurs in a single step. Reactive intermediates or other unstable high energy intermediates are not involved. [1] [2] Concerted reaction rates tend not to depend on solvent polarity ruling out large buildup of charge in the transition state.
An underdamped response is one that oscillates within a decaying envelope. The more underdamped the system, the more oscillations and longer it takes to reach steady-state. Here damping ratio is always less than one. Critically damped A critically damped response is the response that reaches the steady-state value the fastest without being ...