Remember that y(t) = et is the solution to the initial value problem y′ = y, y(0) = 1. Then e = e1, and in MATLAB this is e = exp(1). Suppose we try to calculate e approximately by solving the initial value problem, using the methods of this chapter. Use step sizes of the form 1/n, where n is an integer. For each of Euler’s method, the second order Runge-Kutta method, and the fourth order Runge-Kutta method, how large does n have to be to get an approximation eapp which satisfies |eapp − e| ≤ 10−3?
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