This paper considers family of A(α)-stable second derivative linear multistep methods of order p = k + 3 for step number k ≥ 15 for the solution of stiff IVPs in ODEs. The methods are demonstrated to be A(α)-stable for k ≥ 13. At k = 14, the method is stable but not A(α)-stable. The instability of the new methods sets in when k > 15. Numerical examples are given to demonstrate the application of the methods.
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