The following tables (Tab.13,Tab.14,Tab.15) are of great importance.
Tab.13 is the same as Tab.5 (with "Reduced value y(1)" and "ORD") but brings time evaluation of the computation. For instance, using the 17th method order requires 0.983 ms.
| Reduced value y(1) | ORD | Time (ms) |
| 2. | 1 | 0.084 |
| 2. | 2 | 0.140 |
| 2. | 3 | 0.195 |
| 2.7 | 4 | 0.248 |
| 2.71 | 5 | 0.307 |
| 2.718 | 6 | 0.365 |
| 2.7182 | 7 | 0.422 |
| 2.7182 | 8 | 0.468 |
| 2.718281 | 9 | 0.531 |
| 2.7182818 | 10 | 0.589 |
| 2.71828182 | 11 | 0.649 |
| 2.718281828 | 12 | 0.693 |
| 2.7182818284 | 13 | 0.757 |
| 2.71828182845 | 14 | 0.828 |
| 2.71828182845 | 15 | 0.861 |
| 2.71828182845904 | 16 | 0.911 |
| 2.71828182845904 | 17 | 0.983 |
| 2.71828182845904 | 18 | 1.033 |
Tab.13
If we wanted to reach the same accuracy by the 4th order Runge-Kutta method, we would have to use a substantially shorter integration step and the computation time would be 271.229 ms ( Tab.14).
| h(s) | Reduced value y(1) | Time (ms) |
| 1 | 2.7 | 0.299 |
| 0.1 | 2.7182 | 2.691 |
| 0.01 | 2.718281828 | 27.500 |
| 0.001 | 2.71828182845904 | 271.229 |
Tab.14
Tab.15 shows that it is possible to calculate the differential equation (20) with the integration step as great as 400s, which requires the use of 575 Taylor series terms. The computation takes 31.999 ms.
| h(s) | ORD | Time (ms) |
| 1 | 18 | 1.033 |
| 10 | 43 | 2.504 |
| 20 | 64 | 3.560 |
| 30 | 82 | 4.642 |
| 40 | 99 | 5.551 |
| 50 | 115 | 6.487 |
| 100 | 200 | 11.282 |
| 400 | 575 | 31.999 |
Tab.15
Note: All time evaluations were obtained on the ACA 32000 computer (based on National Semiconductor 32000 processor).