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Amplification and suppression of round-off error in Runge–Kutta methods

A simple nonstiff linear initial-value problem is used to demonstrate the amplification of round-off error in the course of using a second-order Runge–Kutta method. This amplification is understood in terms of an appropriate expression for the global error. An implicit method is then used to show how the roundoff error may actually be suppressed. This article describes a phenomenon not usually considered in general purpose textbooks on numerical analysis, and is therefore potentially interesting and useful to students of the subject.