TIME-DOMAIN ANALYSIS OF NON-LINEAR 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 q continuous derivatives, the derivative of order q+1 being discontinuous, the local truncation error of a k-step backward differentiation formula applied over a discontinuity will be of order q +1 for k > q. For a finite number of discontinuities the order of convergence is q+1 for k>q. For piece wise-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. © 1979 IEEE