# Improved Euler's Method Help

• Nov 8th 2009, 05:58 PM
archer007
Improved Euler's Method Help
I am trying to use the Improved Euler's Method to solve a homework problem, but I am having trouble with the notation and my book is extremely unhelpful.

http://img687.imageshack.us/img687/103/eulers.png
Where the lower formula is the Improved Euler's method.

I am given:

y = 5e^(x(x+2))
y' = 2y(x+1)
y(0) = 5
dx = .3 (I'm guessing this is step size...)

My main difficulty is notation and conception of the problem: the notation is confusing me, and I'm not sure what is actually happening in the formula. Does f(x,y) mean the function with x and y substituted, or something else? The problem asks for the first approximation. If someone could explain the problem in steps that would be great.
• Nov 8th 2009, 10:14 PM
scorpion007
Usually they tell you that \$\displaystyle y'=f(x,y)\$.

So in your case \$\displaystyle f(x,y)=2y(x+1)\$ and \$\displaystyle y_0=y(x_0)=5\$ and \$\displaystyle x_0 = 0\$.

So find \$\displaystyle z_1\$ and then \$\displaystyle y_1, x_1\$, then \$\displaystyle z_2, y_2, x_2\$, etc.

They should probably mention that \$\displaystyle x_n = x_{n-1}+\Delta x\$

(Usually \$\displaystyle h\$ is used for the step size though.)