The Euler's Method equation

**DJ Hobo** · May 12th 2010, 09:05 PM

In the Euler's Method section of my textbook, there are two equations mentioned (see attachment). I was wondering if there was any difference between the two, or if they refer to the same thing.

The help would be appreciated

**HallsofIvy** · May 13th 2010, 04:32 AM

Originally Posted by DJ Hobo

In the Euler's Method section of my textbook, there are two equations mentioned (see attachment). I was wondering if there was any difference between the two, or if they refer to the same thing.

The help would be appreciated

They are different equations the second being more general than the first.

In $y_{n+1}= y_n+ hF(y_n, t_n)$ we are ignoring the fact that t is a continuous variable and just looking at specific points, $t_0, y_0)$ , $(t_1, y_1)$ , etc. separted by distance h along the t axis.

In $y(t+ h)= y(t)+ hy'(t)$ we are retaining the continuity of t- here t could be any number. Of course, if we take $t_0$ to be some specific value, then define $y_0= y(t_0)$ , $t_1= t_0+ h$ , $y_1= y(t_1)$ , $t_2= t_1+ h= t_0+ 2h$ , $y_2= y(t_2)$ , etc. then the second equation becomes the same as the first.

**DJ Hobo** · May 13th 2010, 04:34 AM

Ahh yes, I understand. Thanks for that.

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