We solve it by Euler's method using mesh size  . We compute  and the results are tabulated as follows:
Table-2.2
Effect of Absolute Stability |
h |
N |
y(1) |
1 |
1 |
0 |
0.1 |
10 |
0.9044 E 16 |
0.01 |
100 |
Overflow |
0.001 |
1000 |
0.99999 |
0.0001 |
10000 |
0.99999 |
0.00001 |
100000 |
0.99999 |
|
We can notice that overflow occurs because  for this problem and so with  the error is amplified by  at each step. In 100 steps, the error in the first step is increased by nearly  in size. Once we find  the computed solutions are meaningful and converge to the true solution. |
