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# Otherwise we accept the step and suggest a step size

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Unformatted text preview: procedure that seems to be reasonably robust is to select the initial step size as 1=p h = 1=T p + kf (0 y(0))kp where T is the nal time and p = p + 1 for local error control and p = p for local error per unit step control. Example 3.5.6. ( 16], Section II.4). We report results when several explicit fourthorder explicit Runge-Kutta codes were applied to y1 = 2ty1 log(max(y2 10 3)) y1(0) = 1 y2 = ;2ty2 log(max(y1 10 3)) y2(0) = e: 0 ; ; 0 52 0 1 2 1 2 2 3 2 9 4 9 1 3 7 36 2 9 5 6 1 ; 12 35 ; 144 ; 55 36 35 48 15 8 1 1 ; 360 ; 11 ; 8 1 36 2 41 22 43 1 ; 260 13 156 ; 118 39 1 6 1 10 32 195 80 39 11 11 4 4 13 0 40 40 25 25 200 Table 3.5.1: Butcher's seven-stage sixth-order explicit Runge-Kutta method. 13 200 The exact solution of this problem is y1(t) = esin t2 y2(t) = ecos t2 : Hairer et al. 16] solved the problem on 0 t 5 using tolerances ranging from 10 7 to 10 3. The results presented in Figure 3.5.2 compare the base 10 logarithms of the maximum global error and the number of function evaluation...
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