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By Franz L. Alt (Ed.)

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A($, t ) = b(z, t ) - * .. 25 It follows [30 (properly interpreted), 451 from the Courant Minimax Principle that 51. 11) follows readily. Moreover, these norms arc uniformly comparable with the usual LZnorm, and p = 0. 27) assuming At/Ax to be held fixed. 23) and to other difference equations, including higher order correct equations in some cases. IICkllb 44 JIM DOUGLAS, JR. We see that stability and consistency are sufficient for convergence; Lax and Richtmyer [46, 471 have shown that the converse is essentially true, at least for properly posed pure initial value problems.

Z E aR, U(T, t ) = g(r, t ) , The dimensionality of R is arbitrary. 3) where w, is the vector representing the approximate solution a t the grid points in R a t time tn. Assume that the space increments are functions of At. 3) is explicit in appearance, it still represents the general two-level difference equation, since the multiplier of w , + ~in a n implicit equation must be invertible if the equation is to be practically useful. 1) as the increments of the independent variables tend to zero.

Z E aR, U(T, t ) = g(r, t ) , The dimensionality of R is arbitrary. 3) where w, is the vector representing the approximate solution a t the grid points in R a t time tn. Assume that the space increments are functions of At. 3) is explicit in appearance, it still represents the general two-level difference equation, since the multiplier of w , + ~in a n implicit equation must be invertible if the equation is to be practically useful. 1) as the increments of the independent variables tend to zero.

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