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 + ex. 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%
Answer. a

2. Consider an ordinary differential equation \frac{\mathrm{d} x}{\mathrm{d} t}=4t+4. If x = xo 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
Answer. d
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