By W. F. Ames, M. Ginsberg (auth.), Prof. J. Tinsley Oden (eds.)
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Additional info for Computational Mechanics: International Conference on Computational Methods in Nonlinear Mechanics, Austin, Texas, 1974
At x = O, t > 0 and x > O, t = O. 36) points 1 _< j < N = I / A x , and 0 at the r i g h t boundary. 37) A simple summation shows t h a t t h i s scheme is conservative, the time change of ~ in a region is equal to the f l u x in minus the f l u x out K - u -(n)1 k+l ~ ( n ) + ~k J + provided we stay away from the boundary ( i . e . 36), F~(n) n)I j+l + ~ I 1 ~ J, k < N). 37) is unstable. To see t h i s note t h a t ( 3 . 3 6 ) , ( 3 . 36a) 57 0 -I 1 0 -I K = 1 9 0 -I 2 -I This system admits s o l u t i o n s of the form ~(n) : Xn V , where V is an eigenvector of K and X is a root of X2 - 1 = C~X and p is the eigenvalue associated with V.
L. Keller, A basic theorem in the computation of ellipsoid. al error bounds, Numer. , 19, No. 3, 218 (1972).  R. Bulirsch, and J. Stoer, Asymptotic upper and lower bounds for results of extrapolation methods, Numer. , ~, 93 (1966).  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.
Evidence to reach a conclusion. reduced by the Certainly there is i n s u f f i c i e n t Storage and time considerations may eventually be development of parallel bilateral algorithms or polyalgorithms and/or by the use of hardware or microprogramming assistance. I f time and space requirements prove to be noncompetitive with those of 28 e x i s t i n g nonbounding techniques then the user w i l l be faced with the painful decision of whether he is w i l l i n g to exchange substantial storage and time resources f or accurate bounds.
Computational Mechanics: International Conference on Computational Methods in Nonlinear Mechanics, Austin, Texas, 1974 by W. F. Ames, M. Ginsberg (auth.), Prof. J. Tinsley Oden (eds.)