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Consider an ordinary differential equation dx/dt = 4t + 4. If x = x0 at t = 0, the increment in x calculated using Runge-Kutta fourth order multi-step method with a step size of Δt = 0.2 is

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

Correct answer: 0.88

Solution

Since dx/dt = 4t+4 is linear in t, RK4 reproduces the exact integral over the step: increment = integral_0^0.2 (4t+4) dt = 2(0.2^2)+4(0.2) = 0.08+0.8 = 0.88 (index 3), not 0.44.

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