Now consider a forward difference: u'(t_n) \approx [D_t^+ u]^n = \frac{u^{n+1}-u^n}{\Delta t}\tp Define the truncation error: R^n = [D_t^+ u]^n - u'(t_n)\tp Expand u^{n+1} in a Taylor series around t_n , u(t_{n+1}) = u(t_n) + u'(t_n)\Delta t + {\half}u''(t_n)\Delta t^2 + \Oof{\Delta t^3} \tp We get R = {\half}u''(t_n)\Delta t + \Oof{\Delta t^2}\tp