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Differential EquationsMediumNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Medium problem

A tank with capacity 2020 L starts empty. Water flows in at a rate r(t)=5−0.5tr(t) = 5 - 0.5t L/min (t in minutes). Using Heun's (improved Euler) method with h=2h = 2 minutes for two steps (k1=r(tn)k_1 = r(t_n), k2=r(tn+h)k_2 = r(t_n+h), Vn+1=Vn+h2(k1+k2)V_{n+1} = V_n + \dfrac{h}{2}(k_1+k_2)), estimate the volume in the tank at t=4t = 4 minutes, and find how many liters of capacity remain at that time.