Use each of the Adams-Bashforth methods to approximate the solutions to the following initial-value problems. In each case use starting values obtained from the Runge-Kutta method of order four. Compare the results to the actual values. a. y' = (2 2ty)/(t2 + 1), 0 t 1, y(0) = 1, with h = 0.1 actual solution y(t) = (2t
Use each of the Adams-Bashforth methods to approximate the solutions to the following initial-value problems. In each case use starting values obtained from the Runge-Kutta method of order four. Compare the results to the actual values.
a. y' = (2 − 2ty)/(t2 + 1), 0≤ t ≤ 1, y(0) = 1, with h = 0.1 actual solution y(t) = (2t + 1)/(t2 + 2).
b. y' = y2/(1 + t) , 1≤ t ≤ 2, y(1) = −(ln 2)−1, with h = 0.1 actual solution y(t) =−1/(ln(t + 1)).
c. y' = (y2 + y)/t, 1≤ t ≤ 3, y(1) = −2, with h = 0.2 actual solution y(t) = 2t/(1 - t).
d. y' = −ty + 4t/y, 0≤ t ≤ 1, y(0) = 1, with h = 0.1 actual solution y(t) = √(4 − 3e−t2).
a. y' = (2 − 2ty)/(t2 + 1), 0≤ t ≤ 1, y(0) = 1, with h = 0.1 actual solution y(t) = (2t + 1)/(t2 + 2).
b. y' = y2/(1 + t) , 1≤ t ≤ 2, y(1) = −(ln 2)−1, with h = 0.1 actual solution y(t) =−1/(ln(t + 1)).
c. y' = (y2 + y)/t, 1≤ t ≤ 3, y(1) = −2, with h = 0.2 actual solution y(t) = 2t/(1 - t).
d. y' = −ty + 4t/y, 0≤ t ≤ 1, y(0) = 1, with h = 0.1 actual solution y(t) = √(4 − 3e−t2).
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