THE A-CONTRACTIVE 2ND-ORDER MULTISTEP FORMULAS WITH VARIABLE STEPS

The (k minus 1)-parameter family of all second-order k-step formulas which are A-contractive in the max norm is derived for arbitrary variable integration steps. A-contractive methods are suitable for generating stable numerical solutions of stiff problems which lack smoothness. For example, A-contractive one-leg methods are guaranteed to be stable with respect to dx/dt equals lambda (t)x for any lambda (t) satisfying Re lambda (t) less than equivalent to 0 and arbitrary step sequences left brace h//n right brace . There also is evidence that A-contractive one-leg methods give very accurate amplitude responses when applied with variable steps to certain stiff problems with oscillatory nonstiff modes and little or no dissipation.