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The formal solution for dynamically optimized control of a process is specified in terms of a two-point boundary problem. The numerical computation then presents great difficulties and speed of convergence is vital, even with the most powerful of contemporary computers. The authors give a method for rapid final convergence in which the two-point boundary problem is avoided altogether, although it is in fact only slightly different to methods of second variations. Computing experience with two examples is then described: a) aircraft landing and b) control of a boiler, with which the speed of convergence is well illustrated.