Geodesic
A ($\alpha $)-Stable Linear Multistep Methods for Stiff IVPs in ODEs
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 1, pp. 73-90.

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In this paper, a class of A($\alpha $)-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number $k\le 3$ and stiffly stable for $k=4, 5$ and $6$. Some numerical results are reported to illustrate the method.
Classification : 65L05, 65L06
Keywords: second derivative method; collocation and interpolation; initial value problem; stiff stability; boundary locus 
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Okuonghae, R. I.; Ikhile, M. N. O. A ($\alpha $)-Stable Linear Multistep Methods for Stiff IVPs in ODEs. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 1, pp. 73-90. http://geodesic.mathdoc.fr/item/AUPO_2011__50_1_a6/