Nonlinear fixed-h stability of linear multistep formulas

Stability properties similar to A-stability are established for implicit linear multistep formulas, LMF, when applied to nonlinear stable systems. Sufficient criteria are given which guarantee the fixed-h stability of the global numerical error for various classes of nonlinearities. These criteria relate the behavior of the root-locus curve defined by the LMF to the dissipative properties of the system. A simple criterion for the stability of a composite system is also given. © 1977.