A count of the number of evaluations of the function f used in solving the initial-value problem

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A count of the number of evaluations of the function f used in solving the initial-value problem y' = f (x, y), y(x0) = y0 is used as a measure of the computational complexity of a numerical method. Determine the number of evaluations of f required for each step of Euler’s, the improved Euler’s, and the RK4 methods. By considering some specific examples, compare the accuracy of these methods when used with comparable computational complexities.

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