Picard's method for solving the initial-value problem y' = f (t, y), a t b, y(a) = , is described as follows: Let

Picard's method for solving the initial-value problem
y' = f (t, y), a ‰¤ t ‰¤ b, y(a) = α,
is described as follows: Let y0(t) = α for each t in [a, b]. Define a sequence {yk(t)} of functions

a. Integrate y' = f (t, y(t)), and use the initial condition to derive Picard's method.
b. Generate y0(t), y1(t), y2(t), and y3(t) for the initial-value problem
y' = ˆ’y + t + 1, 0 ‰¤ t ‰¤ 1, y(0) = 1.

nf yk (t)-+/ f(t.yk-I(t)) dr, k-1,2,