A family of highly stable second derivative block methods for stiff IVPs in ODEs

This paper considers a class of highly stable block methods for numerically solving 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 ( α )-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 the second derivative linear multistep method in [8].