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 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].