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Differential EquationsChallengeNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Challenge problem

For the decay equation y′=−2yy' = -2y, Euler's method yn+1=(1−2h)yny_{n+1} = (1 - 2h)y_n is stable (iterates shrink) only while ∣1−2h∣<1|1 - 2h| < 1. Find the critical step size hh where stability is lost.