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Whenever f satisfies certain smoothness conditions, there is always a sufficiently small step size h such that the difference between the real function value Yi+1 at ti+1 and the approximation Xi+1 is less than some required error magnitude ?. [e.g. Burden and Faires]
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Euler's method: very quick as one computation of the derivative function f at each step.
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Other methods require more computation per step size h but can produce the specified error ? with fewer steps as can use a larger value of h. Thus Euler's method is not best.
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