Time-domain analysis of nonlinear systems with finite number of continuous derivatives

The application of the backward differentiation formulas to the solution of dynamic systems which are modeled by nonlinear functions with a finite number of continuous derivatives is studied. It is shown that if the functions have continuous derivatives, the derivative of order being discontinuous, the local truncation error of a -step backward differentiation formula applied over a discontinuity will be of order for . For a finite number of discontinuities the order of convergence is for . For piecewise-linear (pwl) systems the order of the formulas is therefore restricted to 2. Practical expressions for computing estimates of the local truncation error when a second-order formula is applied to pwl systems are given.