Question

Runge-kutta (order four) to approximate the solution of the initial-value problem y = f (t, y), a ≤ t ≤ b, y(a) = α, at (n + 1) equally spaced numbers in the interval [a, b]: input endpoints a, b; integer n; initial condition α. Output approximation w to y at the (n + 1) values of t. Step 1 set h = (b − a)/n; t = a; w = α; output (t, w). Step 2 for i = 1, 2, ... , n do steps 3–5. Step 3 set k1 = hf (t, w); k2 = hf (t + h/2, w + k1/2); k3 = hf (t + h/2, w + k2/2); k4 = hf (t + h, w + k3). Step 4 set w = w + (k1 + 2k2 + 2k3 + k4)/6; (compute wi.) t = a + ih. (compute ti.) step 5 output (t, w). Step 6 stop.

Answer 1

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