Although numerous writers have stated that the class of single-step ("Runge-Kutta"~like) methods of numerical integration of ordinary differential equations are stable under calculational or round-off error, no one has given formal. equations for the bounds on the propagated error to indicate this stability. Rutishauser [1] justifies the stability by noting that there is only one solution to the approximating difference equation, and Hildebrand [2] calculates a propagated error bound for the simplest (Euler) case. However, the latter bound does not indicate the stability for even that case.It is the purpose of this paper to investigate this "stability" of the Kutta fourth order orocedure for integration of the ordinary differential equation *
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