# Notation in numerical methods

What are the differences in using $h$ and $\triangle t$ to represent a time step?

-
$\Delta t$ is older. It marries well with the Leibniz notation with the derivative. The $\Delta$ is a constant reminder of the meaning. But it takes more space. Apart from that, no difference. If there are several variables, not just time, $\Delta x$, $\Delta y$, $\Delta t$ can be useful. – André Nicolas Apr 27 '13 at 14:14
Thanks a lot. Was really bugging me not know and quite a difficult thing to find out. – Kane Blackburn Apr 27 '13 at 14:16

## 1 Answer

Typically, we have:

$$h = \frac{b - a}{N}$$

from the given interval of the problem.

In some numerical methods however, we have both $h$ and $t$ show up in the solution, so care should be taken with those.

For example, in Runge-Kutta, we have $h$ and $t$.

• $h$ is as given above
• $t_0$ starts at a
• $t_i = a + ih$

Otherwise, they are effectively the same and the delta notation is old school.

-
Right to the point! $\large +1^\checkmark$ – amWhy Apr 28 '13 at 0:10