Discuss consistency, stability, and convergence for the Implicit Trapezoidal method
wi+1 = wi + h/2 (f (ti+1,wi+1) + f (ti ,wi)) , for i = 0, 1, . . . , N − 1,
With w0 = α applied to the differential equation
y = f (t, y), a ≤ t ≤ b, y(a) = α.
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