To examine absolute stability of the Euler's method, we consider the test equation For this, we get

(2.20)

The true solution of is

, so that by Taylor's series

(2.21)

Let , we have from (2.20)

and therefore from (2.20) & (2.21), we have

Or

(2.22)

The first expression on the RHS of (2.22) gives the local truncation error and the second expression is the inherited error.