Question: Use the Trapezoid method to analysis. Consider a scalar ODE x(t) = f(t, x(t) ) starting from x(0). Then, the trajectory x(t) over t E

Use the Trapezoid method to analysis.

Consider a scalar ODE x(t) = f(t, x(t) ) starting from x(0). Then, the trajectory x(t) over t E [0, T] satisfies x ( tn+1 ) = a(tn) + / (T=tn+1 T = tn f (T, a(T) ) dr for tn = nh. Let g(T) := f(T, x(T)). Assume that g is twice continuously differentiable over [0, T]. (a) If 0

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