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By Despres B.

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Extra resources for Analyse numerique matricielle (DEA P6)

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3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . 4 Experimental Results. . . . . . . . . . . . . . . . . . . . . . 5 Error Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 6 Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Generator Matrix . . . . . . . . . . . . . . . . . . . 2 Time Stepping . . . .

3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . 4 Experimental Results. . . . . . . . . . . . . . . . . . . . . . 5 Error Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 6 Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Generator Matrix . . . . . . . . . . . . . . . . . . . 2 Time Stepping . . . . . . . . . . . . . . . . .

T. j = i, ai j = 0. 1 is bounded as follows: A−rI PROOF ≤ 1 max tr (xi ) + r. 4a), we find tr (xi ) = ai j tr (x j − xi )(x j − xi ) j =i = a i j x j − xi 2 j =i ≥ ε2 ai j . 7). 1 can be combined to give a stability condition in terms of the ratio between the time step and the minimum point separation. 1 holds provided that δt 1 − r δt . 8) P1: Naresh July 31, 2007 18:59 28 C925X C925X˙C002 CHAPTER 2 The lemma indicates that, if the number of grid points is increased so that the distances between grid points are reduced by a factor c , then for stability reasons, the number of time steps should be increased by a factor c 2 .

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