Good Test Equation for Computer or Calculator Although the growth equation y′ = ky is simple, it is not easy to approximate numerically, particularly over intervals [0, a) for large a. Compare the accuracy of different numerical methods by solving the IVP y′ = y, y(0) = 1, and evaluating the solution at t = 1. The exact value of y(1) is e, so all methods can be compared against this value. Try step sizes of 0.1, 0.5, and 1. Although a step size of 1 is enormous, you may be surprised at the accuracy of certain other methods even so—comment on why this might be so.
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