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ISBN-10: 0120121034

ISBN-13: 9780120121038

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The derivation of these higher order terms is extremely laborious, the correctness of the expansion is difficult to establish, and the programming of the method is extremely involved. 4"where small divisor problems arise. Even for noncritical orbits, the accuracy is limited and for short term prediction cannot be as accurate as numerical integration. A large number of general perturbation methods, have been proposed. The classical theories of Hansen and Delaunay have been modified so as to apply to the artificial satellite problem, the former by Dr.

One suggestion is that the integration for yt+l be performed first with a step of length h and then with two steps of length h / 2 . This will yield 2 values for yt+l. The difference between these two values then provides a reasonable estimate of the local truncation error. This method requires three times as much computing per step and for this reason cannot be seriously considered. Another suggestion is the following : having obtained three successive equally spaced values yIP1, y E ,yz+l,usc Simpson’s rule over the two intervals to obtain a new estimate of yz u;+1 = 2/* + h ( y L 1 + 2y’, + yE+d which has the same local truncation error as the Runge-Kutta method.

The flexibility features affect both the speed of the integration and the accuracy of the results. Frequent interruption of the basic integrating routine results in increased computing time because the restarting procedure, except for Runge-Kutta methods, is expensive and also tends to reduce accuracy although the exact reason for this is not clear. I n discussing the various integration methods emphasis will be placed on the factors which affect speed and on the errors-round-off and truncation-which affect accuracy.

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Advances in Computers, Vol. 3


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