Euler integration is the simplest and most obvious way to numerically integrate a set of differential equations. Euler integration consists of the following steps:
| 1. | Set Time to its initial value. |
| 2. | Initialize the levels. |
| 3. | Compute the rates of change of the Levels at the current value of Time. |
| 4. | Use the rates of change to compute the Levels at Time + TIME STEP according to the formula: |
LEVELTime+TIME STEP = LEVELTime + TIME STEP * RATETime
| 5. | Add TIME STEP to Time. |
| 6. | Repeat steps 3-5 until Time is equal to FINAL TIME. |
See Computational Sequence for more information.
Euler integration assumes that the rates computed at a given time are constant through the time interval (TIME STEP). In general, this is not likely to be true, and that is why Euler integration is not very accurate.
The error made in using Euler integration is proportional to the square of TIME STEP on an integration step and proportional to TIME STEP over the whole simulation. To make the integration more accurate, you can decrease TIME STEP. Although Euler integration is not a good technique for getting accurate solutions to differential equations, for many business and social models where the distinction between difference and differential equations is blurry, Euler integration is appropriate.
