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By W. F. Ames, M. Ginsberg (auth.), Prof. J. Tinsley Oden (eds.)

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Keller, A basic theorem in the computation of ellipsoid. al error bounds, Numer. , 19, No. 3, 218 (1972). [31] R. Bulirsch, and J. Stoer, Asymptotic upper and lower bounds for results of extrapolation methods, Numer. , ~, 93 (1966). [32] A. D. Gorbunov, and Y. A. Shakhov, On the approximate solution of Cauchy's problem for ordinary d i f f e r e n t i a l equations to a given number of correct figures, Parts I and I I , USSRComputation Mathematics and Mathematical Physics, 3, No. 2, 316 (1963) and ~, No.

4 S t a b i l i t y of P o i s e u i l l e Flow. This problem has been considered by many authors both as a steady state and as a t r a n s i e n t problem. Various entry and e x i t conditions have been supposed and an algorithm has been considered successf u l when i t converges to a steady state. Apart from an occasional disclaimer to the e f f e c t that a solution may not represent a real flow, l i t t l e a t t e n t i o n has been given to the question of physical s t a b i l i t y as d i s t i n c t from numerical s t a b i l i t y .

210 as the degrees o f freedom went from 3 to 36 (N = l to 7). 209 so t h a t i t appears t h a t the i t e r a t i v e s o l u t i o n diverges f o r Reynolds numbers of the order 15 based on the width and c e n t r a l v e l o c i t y . This e x p l a i n s the f a i l u r e of the steady state c a l c u l a t i o n s with TUBA 6 at higher Reynolds Numbers. I t is noteworthy t h a t the lack o f a real r o o t is analogous to the f a c t t h a t a p l a t e b u i l t - i n edges has no real divergence speed.

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