Runge Kutta Method MCQ

1. Consider the first order initial value problem

y’ = y + 2x – x², y(0) = 1, (0 ≤ x < ∞) with exact solution y(x) = x² + e^x. For x = 0.1, the percentage diference between the exact solution and the solution obtained using a single iteration of the second-order Runge Kutta method with step size h = 0.1 is

1. 0.06%
2. 0.07%
3. 0.08%
4. 0.1%

2. Consider an ordinary differential equation $\frac{\mathrm{d} x}{\mathrm{d} t}=4t+4$. If x = x_o at t = 0, the increment in x calculated using Runge Kutta fourth order multistep method with a step size of Δt = 0.2 is

1. 0.22
2. 0.44
3. 0.66
4. 0.88