# euler's method

• Apr 21st 2008, 01:06 PM
bbco88
euler's method
Im just not understanding euler's method at all, can someone please help me... I have a homework question that says....
apply euler's method to the differenctial equation to estimate the solution at t=1, starting from the given initial condition. First use one step with Change of t=1 (you know the triangle before t=1), and then use two steps with the change of t=5

dw/dt=2/1+t, with initial condition w(0)=3

also I have applied the euler method into my calculator to check my answers, but Im not sure how to work it, can anyone walk me through how to work it on my ti-83 plus
• Apr 22nd 2008, 02:37 AM
CaptainBlack
Quote:

Originally Posted by bbco88
Im just not understanding euler's method at all, can someone please help me... I have a homework question that says....
apply euler's method to the differenctial equation to estimate the solution at t=1, starting from the given initial condition. First use one step with Change of t=1 (you know the triangle before t=1), and then use two steps with the change of t=5

dw/dt=2/1+t, with initial condition w(0)=3

also I have applied the euler method into my calculator to check my answers, but Im not sure how to work it, can anyone walk me through how to work it on my ti-83 plus

With Eulers method you step from a known value of the function to a new value using the stepping formula:

$\displaystyle w(t_1+\delta)=w(t_1)+\delta \left. \frac{dw}{dt} \right|_{t=t_1}$

For the one step case we have $\displaystyle t_1=0$, and $\displaystyle \left. \frac{dw}{dt} \right|_{t=0}=2$ and $\displaystyle \delta=1$.

For the two step process you first do a single step from $\displaystyle t=0$ to $\displaystyle t=2.5$. Then you use your estimate for $\displaystyle w(2.5)$ as the starting point for a second step from $\displaystyle t=2.5$ to $\displaystyle t=5$.

RonL