The STEP5 function provides approximation to the Heaviside step function with a quintic polynomial. It has continuous first and second derivatives. Its third derivative is discontinuous at x=x0 and x=x1.
STEP5 (x, x0, h0, x1, h1)
| x | The independent variable. |
| x0 | A real variable that specifies the x value at which the STEP5 function begins. |
| x1 | A real variable that specifies the x value at which the STEP5 function ends. |
| h0 | The initial value of the step. |
| h1 | The final value of the step. |
The figure shown next illustrates the STEP5 function.
STEP5 Function
The equation defining the STEP5 function is:
= h1 - h0
= (x - x0)/(x1 - x0)
STEP5(TIME, 1, 0, 2, 1)
This function defines a smooth step function from TIME=1 to TIME=2 with a displacement from 0 to 1.