Geodesic
Synthesis of an implicit A-stable one-step second order schemes by the high order backward differentiation formulas
Matematičeskoe modelirovanie, Tome 21 (2009) no. 10, pp. 107-110.

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A routine ode23tb of MATLAB can be made more accurate and stable coincidentally by adding steps of 3-d and 4-th order backward differentiation formulas. 
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V. N. Biryukov. Synthesis of an implicit A-stable one-step second order schemes by the high order backward differentiation formulas. Matematičeskoe modelirovanie, Tome 21 (2009) no. 10, pp. 107-110. http://geodesic.mathdoc.fr/item/MM_2009_21_10_a10/

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