If we now attempt to solve this problem by Euler's method with in the range with given by the exact solution. We find that for the given problem in the range , the choice of causes to lie outside the region of absolute stability, which is the circle with center radius 1, and it follows that for to lie within for all three values of , we must satisfy . Note that the eigen values responsible for this severe restriction in are that is, the very eigen values whose contributions to the theoretical solution are negligible in the range

On the other hand, consider the IVP

where

whose theoretical solution

is, in the range , virtually indistinguishable from that of the previous problem, is integrated perfectly satisfactorily by Euler's rule with step length . The Eigen values of the system for this problem are and for absolute stability we require only .