MathCastle
Differential EquationsChallengeNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Challenge problem

The stiff decay problem y′=−40yy' = -40y, y(0)=1y(0) = 1 (exact solution e−40te^{-40t}) is integrated by the trapezoidal method yn+1=yn+h2(f(tn,yn)+f(tn+1,yn+1))y_{n+1} = y_n + \dfrac{h}{2}\left(f(t_n, y_n) + f(t_{n+1}, y_{n+1})\right) with h=110h = \dfrac{1}{10}. What is the computed estimate of y(0.3)y(0.3)? Express your answer as a common fraction.