Linear damping \beta u' , nonlinear spring force s(u) , and excitation F : \begin{equation} mu'' + \beta u' + s(u) =F(t)\tp \tag{38} \end{equation} 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}