Geodesic
A class of $A(\alpha)$-stable numerical methods for stiff problems in ordinary differential equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 4, pp. 347-364

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The $A(\alpha)$-stable numerical methods (ANM) for the number of steps $k\le7$ for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) are proposed. The discrete schemes proposed from their equivalent continuous schemes are obtained. The scaled time variable $t$ in a continuous method, which determines the discrete coefficients of the discrete method is chosen in such a way as to ensure that the discrete scheme attains a high order and $A(\alpha)$-stability. We select the value of $\alpha$ for which the schemes proposed are absolutely stable. The new algorithms are found to have a comparable accuracy with that of the backward differentiation formula (BDF) discussed in [12] which implements the Ode15s in the Matlab suite. 
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     author = {R. I. Okuonghae},
     title = {A class of $A(\alpha)$-stable numerical methods for stiff problems in ordinary differential equations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {347--364},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2013_16_4_a4/}
}
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R. I. Okuonghae. A class of $A(\alpha)$-stable numerical methods for stiff problems in ordinary differential equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 4, pp. 347-364. http://geodesic.mathdoc.fr/item/SJVM_2013_16_4_a4/