MathCastle
Differential EquationsChallengeNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Challenge problem

An adaptive RK4 code models the local error of a step of size hh as Ch5Ch^5. A trial step with h=0.2h = 0.2 has estimated local error 3.2×10−53.2 \times 10^{-5}. The code accepts a step only if its local error is at most 10−5⋅h10^{-5} \cdot h (error per unit step at most 10−510^{-5}). Using the model, what is the largest step size it can accept? Express your answer as a decimal.