Repeat Exercise 3 using Heuns method. In Exercise 3 a. y' = y/t (y/t) 2 ,
Question:
Repeat Exercise 3 using Heun’s method.
In Exercise 3
a. y' = y/t − (y/t)2, 1≤ t ≤ 2, y(1) = 1, with h = 0.1; actual solution y(t) = t/(1 + ln t).
b. y' = 1+y/t +(y/t)2, 1≤ t ≤ 3, y(1) = 0, with h = 0.2; actual solution y(t) = t tan(ln t).
c. y' = −(y + 1)(y + 3), 0 ≤ t ≤ 2, y(0) = −2, with h = 0.2; actual solution y(t) = −3 + 2(1 + e−2t)−1.
d. y' = −5y+5t2+2t, 0≤ t ≤ 1, y(0) = 1/3 , with h = 0.1; actual solution y(t) = t2+ 1/3 e−5t .
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