Geodesic
A family of highly stable second derivative block methods for stiff IVPs in ODEs
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 1, pp. 67-81

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This paper considers a class of highly stable block methods for the numerical solution of initial value problems (IVPs) in ordinary differential equations (ODEs). The boundary locus of the proposed parallel one-block, $r$-output point algorithms shows that the new schemes are $A$-stable for output points $r=2(2)8$ and $A(\alpha)$-stable for output points $r=10(2)20$, where $r$ is the number of processors in a particular block method in the family. Numerical results of the block methods are compared with a second derivative linear multistep method in [8]. 
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     author = {R. I. Okuonghae and M. N. O. Ikhile},
     title = {A family of highly stable second derivative block methods for stiff {IVPs} in {ODEs}},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     publisher = {mathdoc},
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     number = {1},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2014_17_1_a5/}
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R. I. Okuonghae; M. N. O. Ikhile. A family of highly stable second derivative block methods for stiff IVPs in ODEs. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 1, pp. 67-81. http://geodesic.mathdoc.fr/item/SJVM_2014_17_1_a5/