Stability Mountains for Hansen's Formulas

Here we analyze the two methods from Eldon Hansen (1969) . These are two cyclic linear multistep methods of order $p=5$ and $p=7$. The first one only needs 3 starting values for order 5. The second one only need 4 starting values and reaches order 7. Both methods break the first Dahlquist barrier. They can do that because the Dahlquist barrier only holds for "simple" multistep methods, not for…