Question: One possible third-order RungeKutta method is given by where By analyzing the linear problem determine the function f (h) appearing in the criterion for stable

One possible third-order Runge–Kutta method is given by Yi+1=Yi (k + 4k2 + k3) h 6

where k = f(xi, yi) k = f(xi +0.5h, y; + 0.5hk) k3 = f(xi +h, yi - hk + 2hk2)

By analyzing the linear problem dy dt = , < 0

determine the function f (hλ) appearing in the criterion |f(h)| 1

for stable integration. You do not need to actually compute the maximum step size, as this would be best done using a computer. What numerical method would you use to compute the largest step size?

Yi+1=Yi (k + 4k2 + k3) h 6

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