Linear damping βu′, nonlinear spring force s(u), and excitation F: mu″ Central difference discretization: \begin{equation} [mD_tD_t u + \beta D_{2t} u + s(u)=F]^n \tp \end{equation} Truncation error is defined by \begin{equation} [mD_tD_t \uex + \beta D_{2t} \uex + s(\uex)=F + R]^n \tp \end{equation}