Abstract
This report describes and illustrates a new nonlinear single-step implicit method for the numerical integra tion of general differential systems. The method is A-stable, operates with fixed or variable step size, is computationally fast, and has accuracy comparable to or better than that of other widely used methods. This paper reports computational experiments using this new method and compares the results with those obtained using other integration algorithms, includ ing high-order methods. The comparisons are generally favorable to the new method. The method is applicable to both "stiff" and "nonstiff" systems. On stiff systems the new method was much more accurate than any of the other algorithms tested.
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