W. Liniger

In the numerical solution of ordinary differential equations, certain implicit linear multistep formulas, i.e. formulas of type ∑kj=0 &agr;jxn+j - h ∑kj=0 &bgr;jxn+j = 0, (1) with &bgr;k> ≠ 0, have long been favored because they exhibit strong (fixed-h) stability. Lately, it has been observed [1-3] that some special methods of this type are unconditionally fixed-h stable with respect to the step size. This property is of great importance for the efficient solution of stiff [4] systems of differential equations, i.e. systems with widely separated time constants. Such special methods make it possible to integrate stiff systems using a step size which is large relative to the rate of change of the fast-varying components of the solution.