\(A_ 0\)-stable linear multistep formulas of the \(\alpha\)-type
This paper examines the \(A_ 0\)-stability of the k-step order k linear multistep method of the form \[ y_{n+k}-\alpha y_{n+k-1}+(\alpha - 1)y_{n+k-2}=h\sum^{k}_{i=0}\beta_ iy'_{n+i}. \] All \(A_ 0\)- stable methods of order 4 or less are found and it is shown that there are no \(A_ 0\)-stable k-step methods of order 5 or more of the above form.
scientific article; zbMATH DE number 4018269