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: <math>\tilde{y}_{g} = y_i + h f(t_i,y_i)</math>
next improve the initial guess through iteration of the trapezoidal rule,
: <math>\tilde{y}_{g+1} = y_i + \frac{h}{2}(f(t_i, y_i) + f(t_{i+1},\tilde{y}_{g})).</math>
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