CONVERGENCE AND STABILITY OF STEP-BY-STEP INTEGRATION FOR MODEL WITH NEGATIVE-STIFFNESS.

Convergence conditions and stability conditions 1,2 or 3 were established. The numerical stability of the integration under negative-stiffness belongs to the category of relative stability; consequently, the concepts and the conclusions concerning numerical stability in the case of positive-stiffness (which belongs to absolute stability) cannot be used. The central difference method is convergent and unconditionally stable in the case of negative-stiffness, though it is only conditionally stable in the case of positive-stiffness. The Houbolt method satisfies the requirement for convergence; its stability, however, depends not only on the integration step size DELTA t but also on the stiffness ratio beta for the model with negative-stiffness, unlike the unconditional stability for the model with positive-stiffness. The Newmark constant acceleration method is convergent and unconditionally stable in the case of negative-stiffness just like it is in the case of positive-stiffness.